Question 11 Mark
Find the product of the following binomial:
$\Big(\frac{4\text{x}}{5}−\frac{3\text{y}}{4}\Big)\Big(\frac{4\text{x}}{5}+\frac{3\text{y}}{4}\Big)$
AnswerWe will use the identify $(a+b)^2=a^2+2 a b+b^2$in the given expression to find the product.
$\Big(\frac{4\text{x}}{5}−\frac{3\text{y}}{4}\Big)\Big(\frac{4\text{x}}{5}+\frac{3\text{y}}{4}\Big)$
$=\big(\frac{4\text{x}}{5}\big)^2−\big(\frac{3\text{y}}{4}\big)^2$
$=\frac{16\text{x}^2}{25}−\frac{9\text{y}^2}{16}$
View full question & answer→Question 21 Mark
Write the following squares of binomials as trinomials:
$\big(\frac{3\text{a}}{2}−\frac{5\text{b}}{4}\big)^2$
AnswerWe will use the identities $(a+b)^2=a^2+2 a b+b^2$ and $(a-b)^2=a^2-2 a b+b^2$ to convert the squares of binomials as trinomials.
$\big(\frac{3\text{a}}{2}−\frac{5\text{b}}{4}\big)^2$
$=\big(\frac{3\text{a}}{2}\big)^2−2\big(\frac{3\text{a}}{2}\big)\big(\frac{5\text{b}}{4}\big)+\big(\frac{5\text{b}}{4}\big)^2$
$=\frac{9\text{a}^2}{4}−\frac{15\text{ab}}{4}+\frac{25\text{b}^2}{16}$
View full question & answer→Question 31 Mark
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category?
$p^2 q+p q^2$
AnswerDefinitions: A polynomial is monomial if it has exactly one term. It is called binomial if it has exactly two non-zero terms.
A polynomial is a trinomial if it has exactly three non-zero terms. The polynomial $p^2 q+p q^2$ has exactly two terms, i.e.,$p^2 q$ and $p q^2$. Therefore, it is a binomial.
View full question & answer→Question 41 Mark
Write the following squares of binomials as trinomials:
$\big(9\text{a}+\frac{1}{6}\big)^2$
AnswerWe will use the identities $(a+b)^2=a^2+2 a b+b^2$ and $(a-b)^2=a^2-2 a b+b^2$ to convert the squares of binomials as trinomials.
$\big(9\text{a}+\frac{1}{6}\big)^2$
$=(9\text{a})^2+2(9\text{a})\big(\frac{1}{6}\big)+\big(\frac{1}{6}\big)^2$
$=81\text{a}^2+3\text{a}+\frac{1}{36}$
View full question & answer→Question 51 Mark
Write the following squares of binomials as trinomials:
$\big(3\text{x}−\frac{1}{3\text{x}}\big)^2$
AnswerWe will use the identities $(a+b)^2=a^2+2 a b+b^2$ and $(a-b)^2=a^2-2 a b+b^2$ to convert the squares of binomials as trinomials.
$\big(3\text{x}−\frac{1}{3\text{x}}\big)^2$
$=(3\text{x})^2−2(3\text{x})\big(\frac{1}{3}\text{x}\big)+\big(\frac{1}{3\text{x}})^2$
$=9\text{x}^2−2+\frac{1}{9\text{x}^2}$
View full question & answer→Question 61 Mark
Write the following squares of binomials as trinomials:
$\big(\frac{2\text{a}}{3\text{b}}+\frac{2\text{b}}{3\text{a}}\big)^2$
AnswerWe will use the identities $(a+b)^2=a^2+2 a b+b^2$ and $(a-b)^2=a^2-2 a b+b^2$ to convert the squares of binomials as trinomials.
$\big(\frac{2\text{a}}{3\text{b}}+\frac{2\text{b}}{3\text{a}}\big)^2$
$=\big(\frac{2\text{a}}{3\text{b}}\big)^2+2\big(\frac{2\text{a}}{3\text{b}}\big)\big(\frac{2\text{b}}{3\text{a}}\big)+\big(\frac{2\text{b}}{3\text{a}}\big)^2$
$=\frac{4\text{a}^2}{9\text{b}^2}+\frac{8}{9}+\frac{4\text{b}^2}{9\text{a}^2}$
View full question & answer→Question 71 Mark
Identify the terms, thier coefficients following expressions: $0.2x - 0.3xy + 0.5y$
AnswerDefinitions: A term in an algebraic expression can be a constant, a variable or a product of constants and variables separated by the signs of addition $(+)$ or subtraction $(-).$ Examples: $27,\text{x},\text{xyz},\big(\frac{1}{2}\big)\text{x}^2\text{yz}$ etc.
The expression $0.2x - 0.3xy + 0.5y$ consists of three terms i.e., $0.2x, −0.3xy$ and $0.5y.$ The coefficient of $0.2x$ is $0.2$ The coefficient of $−0.3xy$ is $−0.3, $and the coefficient of $0.5y$ is $0.5.$
View full question & answer→Question 81 Mark
Identify the terms, thier coefficients following expressions:
$7 x^2 y z-5 x y$
AnswerDefinitions: A term in an algebraic expression can be a constant, a variable or a product of constants and variables separated by the signs of addition $(+)$ or subtraction $(-).$ Examples: $27,\text{x},\text{xyz},\big(\frac{1}{2}\big)\text{x}^2\text{yz}$ etc.
The expression $7 x^2 y z-5 x y$ consists of two terms, i.e, $7 x^2 y z$ and $-5 x y$. The coefficient of $7 x^2 y z$ is $7$ and the coefficient of $-5 x y$ is $-5$ .
View full question & answer→Question 91 Mark
Write the following squares of binomials as trinomials:
$\left(a^2 b-b c^2\right)^2$
AnswerWe will use the identities $(a+b)^2=a^2+2 a b+b^2$ and $(a-b)^2=a^2-2 a b+b^2$ to convert the squares of binomials as trinomials.
$\left(a^2 b-b c^2\right)^2$
$=\left(a^2 b\right)^2-2\left(a^2 b\right)\left(b c^2\right)+\left(b c^2\right)^2$
$=a^4 b^2-2 a^2 b^2 c^2+b^2 c^4$
View full question & answer→Question 101 Mark
Identify the terms, thier coefficients following expressions:
$3 x^2 y^2-5 x^2 y^2 z^2+z^2$
AnswerDefinitions: A term in an algebraic expression can be a constant, a variable or a product of constants and variables separated by the signs of addition $(+)$ or subtraction $(-).$
Examples: $27,\text{x},\text{xyz},\big(\frac{1}{2}\big)\text{x}^2\text{yz}$ etc.
The expression $3 x^2 y^2-5 x^2 y^2 z^2+z^2$ consists of three terms, i.e, $3 x^2 y^2-5 x^2 y^2 z^2$ and $z^2$. The coefficient of $3 x^2 y^2$ term is $3$.
View full question & answer→Question 111 Mark
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category?
$x+x^2+x^3+4 y^4$
AnswerDefinitions: A polynomial is monomial if it has exactly one term. It is called binomial if it has exactly two non-zero terms. A polynomial is a trinomial if it has exactly three non-zero terms.
The polynomial $x+x^2+x^3+4 y^4$ has exactly four terms,i.e. $x, x^2, x^3$ and $x^4$ Therefore, it doesn't belong to any of the categories.
View full question & answer→Question 121 Mark
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category$?$
$x + y$
AnswerDefinitions: A polynomial is monomial if it has exactly one term. It is called binomial if it has exactly two non-zero terms. A polynomial is a trinomial if it has exactly three non-zero terms.
The polynomial $x + y$ has exactly two non zero terms, i.e. $x$ and $y.$ Therefore, it is a binomial.
View full question & answer→Question 131 Mark
Find the product of the following binomial:
$\big(\text{x}^4+\frac{2}{\text{x}^2}\big)\big(\text{x}^4−\frac{2}{\text{x}^2}\big)$
AnswerWe will use the identify $(a+b)^2=a^2+2 a b+b^2$ in the given expression to find the product.
$\big(\text{x}^4+\frac{2}{\text{x}^2}\big)\big(\text{x}^4−\frac{2}{\text{x}^2}\big)$
$=(\text{x}^4)^{2}−\big(\frac{2}{\text{x}^2}\big)^2$
$=\text{x}^8−\frac{4}{\text{x}^4}$
View full question & answer→Question 141 Mark
Find the product of the following binomial:
$\big(2\text{x}+\frac{3}{\text{y}}\big)(2\text{x}−\frac{3}{\text{y}}\big)$
AnswerWe will use the identify $(a+b)^2=a^2+2 a b+b^2$in the given expression to find the product.
$\big(2\text{x}+\frac{3}{\text{y}}\big)(2\text{x}−\frac{3}{\text{y}}\big)$
$=(2\text{x})^2−\big(\frac{3}{\text{y}}\big)^2$
$=4\text{x}^2−\frac{9}{\text{y}^2}$
View full question & answer→Question 151 Mark
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category$?\ 5x - 4y + 3x$
AnswerDefinitions: A polynomial is monomial if it has exactly one term. It is called binomial if it has exactly two non-zero terms. A polynomial is a trinomial if it has exactly three non-zero terms. The polynomial $5x - 4y + 3x$ has exactly three terms, i.e. $5x, -4y$ and $3x.$ Therefore, it is a trinomial.
View full question & answer→Question 161 Mark
Find the product of the following binomial:
$\left(2 a^3+b^3\right)\left(2 a^3-b^3\right)$
AnswerWe will use the identify $(a+b)^2=a^2+2 a b+b^2$ in the given expression to find the product.
$\left(2 a^3+b^3\right)\left(2 a^3-b^3\right)$
$=\left(2 a^3\right)^2-\left(b^3\right)^2$
$=4 a^6-b^6$
View full question & answer→Question 171 Mark
Write the following squares of binomials as trinomials:
$(x + 2)^2$
AnswerWe will use the identities $(a+b)^2=a^2+2 a b+b^2$ and $(a-b)^2=a^2-2 a b+b^2$ to convert the squares of binomials as trinomials.
$(x+2)^2$
$=x^2+2 \times x \times 2+b^2$
$=x^2+4 x+b^2$
View full question & answer→Question 181 Mark
Write the following squares of binomials as trinomials:
$(8a + 3b)^2$
AnswerWe will use the identities $(a+b)^2=a^2+2 a b+b^2$ and $(a-b)^2=a^2-2 a b+b^2$ to convert the squares of binomials as trinomials.
$(8 a+3 b)^2$
$=(8 a)^2+2(8 a)(3 b)+(6 b)^2$
$=64 a^2+48 a b+36 b^2$
View full question & answer→Question 191 Mark
Find the product of the following binomial:
$\big(\text{x}^3+\frac{1}{\text{x}^3}\big)\big(\text{x}^3−\frac{1}{\text{x}^3}\big)$
AnswerWe will use the identify $(a+b)^2=a^2+2 a b+b^2$ in the given expression to find the product.
$\big(\text{x}^3+\frac{1}{\text{x}^3}\big)\big(\text{x}^3−\frac{1}{\text{x}^3}\big)$
$=(\text{x}^3)^2−\big(\frac{1}{\text{x}^3}\big)^2$
$=\text{x}^6−\frac{1}{\text{x}^6}$
View full question & answer→Question 201 Mark
Write the following squares of binomials as trinomials:
$(2m + 1)^2$
AnswerWe will use the identities $(a+b)^2=a^2+2 a b+b^2$ and $(a-b)^2=a^2-2 a b+b^2$ to convert the squares of binomials as trinomials.
$(2 m+1)^2$
$=(2 m)^2+2(2 m)(1)+1^2$
$=4 m^2+4 m+1$
View full question & answer→Question 211 Mark
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category$?\ 1000$
AnswerDefinitions: A polynomial is monomial if it has exactly one term. It is called binomial if it has exactly two non-zero terms. A polynomial is a trinomial if it has exactly three non-zero terms. The polynomial $1000$ has exactly one term, i.e. $1000.$ Therefore, it is a monomial.
View full question & answer→Question 221 Mark
Subtract: $-5xy$ from $12xy$
Answer$12xy - (-5xy) = 12xy + 5xy = 17xy$
View full question & answer→Question 231 Mark
Subtract:
$2 a ^2$ from $-7 a ^2$
Answer$-7 a^2-\left(2 a^2\right) $
$=-7 a^2-2 a^2 $
$=-9a^2$
View full question & answer→Question 241 Mark
Find the product of the following binomial:
$\left(a^2+b c\right)\left(a^2-b c\right)$
AnswerWe will use the identify $(a+b)^2=a^2+2 a b+b^2$ in the given expression to find the product.
$\left(a^2+b c\right)\left(a^2-b c\right)$
$=\left(a^2\right)^2-(b c)^2 $
$=a^4-b^2 c^2$
View full question & answer→Question 251 Mark
Find the product of the following binomial:
$(a + 2b)(a - 2b)$
AnswerWe will use the identify $(a+b)^2=a^2+2 a b+b^2$in the given expression to find the product.
$(a + 2b) (a - 2b)$
$= a^2 - (2b)^2$
$= a^2 - 4b^2$
View full question & answer→Question 261 Mark
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category$?\ 7 + a + 5b$
AnswerDefinitions: A polynomial is monomial if it has exactly one term. It is called binomial if it has exactly two non-zero terms. A polynomial is a trinomial if it has exactly three non-zero terms. The polynomial $7 + a + 5b$ has exactly three terms, i.e. $7, a$ and $5b.$ Therefore, it is a trinomial.
View full question & answer→Question 271 Mark
Identify the terms, thier coefficients following expressions: $\frac{\text{a}}{2}+\frac{\text{b}}{2}-\text{ab}$
AnswerDefinitions: A term in an algebraic expression can be a constant, a variable or a product of constants and variables separated by the signs of addition $(+)$ or subtraction $(-).$ Examples: $27,\text{x},\text{xyz},\big(\frac{1}{2}\big)\text{x}^2\text{yz}$ etc. The expression $\frac{\text{a}}{2}+\frac{\text{b}}{2}-\text{ab}$ consists of three terms , i.e., $\frac{\text{a}}{2},\frac{\text{b}}{2}$ and $-ab$ m and $-ab.$ The coefficient of $\frac{\text{a}}{2} \ \text{is} \ \frac{\text{1}}{2}$. The coefficient of $\frac{\text{b}}{2} \ \text{is} \ \frac{\text{1}}{2}$ and the coefficient of $−ab$ is $-1.$
View full question & answer→Question 281 Mark
Identify the terms, thier coefficients following expressions: $9 - ab + bc - ca$
AnswerDefinitions: A term in an algebraic expression can be a constant, a variable or a product of constants and variables separated by the signs of addition $(+)$ or subtraction $(-).$ Examples: $27,\text{x},\text{xyz},\big(\frac{1}{2}\big)\text{x}^2\text{yz}$ etc. The expression $9 - ab + bc - ca$ consists of four terms, i.e, $9 - ab + bc$ and $-ca.$ The coefficient of the term is $9$ is $9.$ The coefficient of $−ab$ is $-1.$ The coefficient of $bc$ is $1,$ and the coefficient of $-ca$ is $-1.$
View full question & answer→Question 291 Mark
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category?
$4a - 15a^2$
AnswerDefinitions: A polynomial is monomial if it has exactly one term. It is called binomial if it has exactly two non-zero terms. A polynomial is a trinomial if it has exactly three non-zero terms.
The polynomial $4a - 15a^2$ has exactly two terms, i.e. $4a$ and $-15a^2$. Therefore, it is a binomial.
View full question & answer→Question 301 Mark
Write the following squares of binomials as trinomials:
$\big(\text{x}+\frac{\text{x}^2}{2}\big)^2$
AnswerWe will use the identities $(a+b)^2=a^2+2 a b+b^2$and $(a-b)^2=a^2-2 a b+b^2$ to convert the squares of binomials as trinomials.
$\big(\text{x}+\frac{\text{x}^2}{2}\big)^2$
$=\text{x}^2+2\text{x}\big(\frac{\text{x}^2}{2}\big)+\big(\frac{\text{x}^2}{2})^2$
$=\text{x}^2+\text{x}^3+\frac{\text{x}^4}{4}$
View full question & answer→Question 311 Mark
Identify the terms, thier coefficients following expressions:
$x^2 + x + 1$
AnswerDefinitions: A term in an algebraic expression can be a constant, a variable or a product of constants and variables separated by the signs of addition $(+)$ or subtraction $(-).$ Examples: $27,\text{x},\text{xyz},\big(\frac{1}{2}\big)\text{x}^2\text{yz}$ etc.
The expression $x^2 + x + 1$ consists of three terms, i.e, $x^2,x $ and $1. $The coefficient of each term is $1$.
View full question & answer→Question 321 Mark
Write the following squares of binomials as trinomials:
$\left(x^2-a y\right)^2$
AnswerWe will use the identities $(a+b)^2=a^2+2 a b+b^2$and $(a-b)^2=a^2-2 a b+b^2$ to convert the squares of binomials as trinomials.
$\left(x^2-a y\right)^2$
$=\left(x^2\right)^2-2 x^2(\text { ay })+(a y)^2 $
$=x^4-2 x^2 a y+a^2 y^2$
View full question & answer→Question 331 Mark
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category?
$2 y-3 y^2+4 y^3$
AnswerThe polynomial $2 y-3 y^2+4 y^3$ has exactly three terms, i.e. $2 y-3 y^2$and $4y^3$. Therefore, it is a trinomial.
View full question & answer→Question 341 Mark
Write the following squares of binomials as trinomials:
$\big(\frac{\text{x}}{4}−\frac{\text{y}}{3}\big)^2$
AnswerWe will use the identities $(a+b)^2=a^2+2 a b+b^2$ and $(a-b)^2=a^2-2 a b+b^2$ to convert the squares of binomials as trinomials.
$\big(\frac{\text{x}}{4}−\frac{\text{y}}{3}\big)^2$
$=\big(\frac{\text{x}}{4}\big)^2−2\big(\frac{\text{x}}{4}\big)\big(\frac{\text{y}}{3}\big)+\big(\frac{\text{y}}{3})^2$
$=\frac{\text{x}^2}{16}−\frac{1}{6}\text{xy}+\frac{\text{y}^2}{9}$
View full question & answer→Question 351 Mark
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category$?\ pqr$
AnswerDefinitions: A polynomial is monomial if it has exactly one term. It is called binomial if it has exactly two non-zero terms. A polynomial is a trinomial if it has exactly three non-zero terms. The polynomial pqr has exactly one term, i.e., $pqr.$ Therefore, it is a monomial.
View full question & answer→Question 361 Mark
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category$?\ 2p + 2q$
AnswerDefinitions: A polynomial is monomial if it has exactly one term. It is called binomial if it has exactly two non-zero terms. A polynomial is a trinomial if it has exactly three non-zero terms. The polynomial $2p + 2q$ has two terms, i.e., $2p$ and $2q$. Therefore, it is a binomial.
View full question & answer→Question 371 Mark
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category$?\ xy + yz + zt + tx$
AnswerDefinitions: A polynomial is monomial if it has exactly one term. It is called binomial if it has exactly two non-zero terms. A polynomial is a trinomial if it has exactly three non-zero terms. The polynomial $xy + yz + zt + tx$ has exactly four terms $xy, yz, zt$ and $tx.$ Therefore, it doesn't belong to any of the categories.
View full question & answer→Question 381 Mark
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category?
$2b - 3b^2$
AnswerDefinitions: A polynomial is monomial if it has exactly one term. It is called binomial if it has exactly two non-zero terms. A polynomial is a trinomial if it has exactly three non-zero terms.
The polynomial $2b - 3b^2$ has exactly two terms, i.e. $2b$ and $−3b^2$Therefore, it is a binomial.
View full question & answer→