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:
$(8 a+3 b)^2$
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:
$(2 m+1)^2$
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
Answer12xy - (-5xy)
= 12xy + 5xy
= 17xy
View full question & answer→Question 231 Mark
Subtract:
$2 a^2$ from $-7 a^2$
Answer$-7 a^2-\left(2 a^2\right)$
$=-7 a^2-2 a^2$
$=-9 a^2$
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:
$(a+2 b)(a-2 b)$
AnswerWe will use the identify $(a+b)^2=a^2+2 a b+b^2$ in the given expression to find the product.
$(a+2 b)(a-2 b)$
$=a^2-(2 b)^2$
$=a^2-4 b^2$
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?
$4 a-15 a^2$
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 $4 a-15 a^2$ has exactly two terms, i.e. $4 a$ and $-15 a^2$. 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: ${ }^2+ x +1$
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: $27, x , xyz ,\left(\frac{1}{2}\right) x ^2 yz$ 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.
$\left(x^2-a y\right)^2$
$=\left(x^2\right)^2-2 x^2(a y)+(a y)^2$
$=x^4-2 x^2 a y+a^2 y^2$
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 $4 y ^3$. 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?
$2 b-3 b^2$
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 $2 b-3 b^2$ has exactly two terms, i.e. 2 b and $-3 b^2$ Therefore, it is a binomial.
View full question & answer→