Question 12 Marks
Find the product.
$2 x(3 x+5 x y)$
$2 x(3 x+5 x y)$
Answer
View full question & answer→We have, $2 x(3 x+5 x y)=(2 x \times 3 x)+(2 x \times 5 x y)$ $\qquad$[by distributive law]
$=6 x^2+10 x^2 y$
$=6 x^2+10 x^2 y$
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19 questions · timed · auto-graded
Question 22 Marks
Simplify
$(a^2+5)(b^3+3)+5$
$(a^2+5)(b^3+3)+5$
Answer
View full question & answer→$(a^{2}+5)(b^{3}+3)+5$
$=a^2\left(b^3+3\right)+5\left(b^3+3\right)+5 $
$=a^2 b^3+3 a^2+5 b^3+15+5 $
$=a^2 b^3+3 a^2+5 b^3+20\qquad$ [adding like terms]
$=a^2\left(b^3+3\right)+5\left(b^3+3\right)+5 $
$=a^2 b^3+3 a^2+5 b^3+15+5 $
$=a^2 b^3+3 a^2+5 b^3+20\qquad$ [adding like terms]
Question 32 Marks
Simplify
$(x^2-5)(x+5)+25$
$(x^2-5)(x+5)+25$
Answer
View full question & answer→$(x^2-5)(x+5)+25$
$=x^2(x+5)-5(x+5)+25 $
$ =x^3+5 x^2-5 x-25+25 $
$ =x^3+5 x^2-5 x \quad \text {[adding like terms]}$
$=x^2(x+5)-5(x+5)+25 $
$ =x^3+5 x^2-5 x-25+25 $
$ =x^3+5 x^2-5 x \quad \text {[adding like terms]}$
Question 42 Marks
Find the product.
$(x+7y)(7x-y)$
$(x+7y)(7x-y)$
Answer
View full question & answer→$(x+7 y)(7 x-y)$
$=(x) \times(7 x-y)+(7 y) \times(7 x-y) $
$ =(x \times 7 x)-(x \times y)+(7 y \times 7 x)-(7 y \times y) $
$ =7 x^2-x y+49 x y-7 y^2 $
$ =7 x^2+48 x y-7 y^2 \quad \text {[adding like terms]}$
$=(x) \times(7 x-y)+(7 y) \times(7 x-y) $
$ =(x \times 7 x)-(x \times y)+(7 y \times 7 x)-(7 y \times y) $
$ =7 x^2-x y+49 x y-7 y^2 $
$ =7 x^2+48 x y-7 y^2 \quad \text {[adding like terms]}$
Question 52 Marks
Find the product.
$(5-2x)(3+x)$
$(5-2x)(3+x)$
Answer
View full question & answer→$(5-2 x)(3+x)$
$=(5) \times(3+x)-(2 x) \times(3+x) $
$ =(5 \times 3)+(5 \times x)-(2 x \times 3)-(2 x \times x) $
$ =15+5 x-6 x-2 x^2 $
$ =15-x-2 x^2 \quad \text {[adding like terms]}$
$=(5) \times(3+x)-(2 x) \times(3+x) $
$ =(5 \times 3)+(5 \times x)-(2 x \times 3)-(2 x \times x) $
$ =15+5 x-6 x-2 x^2 $
$ =15-x-2 x^2 \quad \text {[adding like terms]}$
Question 62 Marks
Multiply these binomials.
$(2.5l-0.5 m)$ and $(2.5 l+0.5 m)$
$(2.5l-0.5 m)$ and $(2.5 l+0.5 m)$
Answer
View full question & answer→We have, $(2.5 l-0.5 m)$ and $(2.5 l+0.5 m)$
According to the question,
$(2.5 l-0.5 m) \times(2.5 l+0.5 m)$
$=(2.5 l) \times(2.5 l+0.5 m)-0.5 m(2.5 l+0.5 m)$
$=(2.5 l \times 2.5 l) +(2.5 l \times 0.5 m) -(0.5 m \times 2.5 l)-(0.5 m \times 0.5 m)$
$=6.25 l^2+1.25 l m-1.25 l m-0.25 m^2$
$=6.25 l^2-0.25 m^2 \quad \text { [adding like terms] }$
According to the question,
$(2.5 l-0.5 m) \times(2.5 l+0.5 m)$
$=(2.5 l) \times(2.5 l+0.5 m)-0.5 m(2.5 l+0.5 m)$
$=(2.5 l \times 2.5 l) +(2.5 l \times 0.5 m) -(0.5 m \times 2.5 l)-(0.5 m \times 0.5 m)$
$=6.25 l^2+1.25 l m-1.25 l m-0.25 m^2$
$=6.25 l^2-0.25 m^2 \quad \text { [adding like terms] }$
Question 72 Marks
Multiply these binomials.
$(2 x+5)$ and $(4 x-3)$
$(2 x+5)$ and $(4 x-3)$
Answer
View full question & answer→We have, $(2 x+5)$ and $(4 x-3)$
According to the question,
$(2 x+5) \times(4 x-3)$
$=(2 x) \times(4 x-3)+5 \times(4 x-3) $
$ =(2 x \times 4 x)-(2 x \times 3)+(5 \times 4 x)-(5 \times 3) $
$ =8 x^2-6 x+20 x-15 $
$ =8 x^2+14 x-15 \quad \text { [adding like terms] }$
According to the question,
$(2 x+5) \times(4 x-3)$
$=(2 x) \times(4 x-3)+5 \times(4 x-3) $
$ =(2 x \times 4 x)-(2 x \times 3)+(5 \times 4 x)-(5 \times 3) $
$ =8 x^2-6 x+20 x-15 $
$ =8 x^2+14 x-15 \quad \text { [adding like terms] }$
Question 82 Marks
Find the product.
$\left(a^2\right) \times\left(2 a^{22}\right) \times\left(4 a^{26}\right)$
$\left(a^2\right) \times\left(2 a^{22}\right) \times\left(4 a^{26}\right)$
Answer
View full question & answer→We have, $\left(a^2\right) \times\left(2 a^{22}\right) \times\left(4 a^{26}\right)$
$=(1 \times 2 \times 4) \times\left(a^2 \times a^{22} \times a^{26}\right) $
$ =8 \times\left(a^{2+22+26}\right) $
$ =8 a^{50}$
$=(1 \times 2 \times 4) \times\left(a^2 \times a^{22} \times a^{26}\right) $
$ =8 \times\left(a^{2+22+26}\right) $
$ =8 a^{50}$
Question 92 Marks
Carry out the multiplication of the expressions in each of the following pairs
$a^2-9,4 a$
$a^2-9,4 a$
Answer
View full question & answer→We have, $a^2-9$ and $4 a$
$\begin{aligned}\left(a^2-9\right) \times 4 a & =4 a \times\left(a^2-9\right) \quad \text { [by commutative law] } \\& =4 a \times a^2-4 a \times 9=4 a^3-36 a\end{aligned}$
$\begin{aligned}\left(a^2-9\right) \times 4 a & =4 a \times\left(a^2-9\right) \quad \text { [by commutative law] } \\& =4 a \times a^2-4 a \times 9=4 a^3-36 a\end{aligned}$
Question 102 Marks
Carry out the multiplication of the expressions in each of the following pairs
$a b, a-b$
$a b, a-b$
Answer
View full question & answer→We have, $a b$ and $a-b$
$(a b) \times(a-b)=(a b) \times(a)-(a b) \times(b)=a^2 b-a b^2$
$(a b) \times(a-b)=(a b) \times(a)-(a b) \times(b)=a^2 b-a b^2$
Question 112 Marks
Carry out the multiplication of the expressions in each of the following pairs
$4 p, q+r$
$4 p, q+r$
Answer
View full question & answer→We have, $4 p$ and $q+r$
$(4 p) \times(q+r)=(4 p \times q)+(4 p \times r)=4 p q+4 p r$
$(4 p) \times(q+r)=(4 p \times q)+(4 p \times r)=4 p q+4 p r$
Question 122 Marks
Obtain the product of
$a,-a^2, a^3$
$a,-a^2, a^3$
Answer
View full question & answer→We have, $a,-a^2$ and $a^3$
$\begin{aligned} \text { Required product } & =(a) \times\left(-a^2\right) \times\left(a^3\right) \\ & =-\left(a \times a^2 \times a^3\right)=-a^6\end{aligned}$
$\begin{aligned} \text { Required product } & =(a) \times\left(-a^2\right) \times\left(a^3\right) \\ & =-\left(a \times a^2 \times a^3\right)=-a^6\end{aligned}$
Question 132 Marks
Obtain the product of
$x y, y z, z x$
$x y, y z, z x$
Answer
View full question & answer→We have, xy, yz and zx
$\begin{aligned} \text { Required product } & =(x y) \times(y z) \times(z x) \\ & =x \times(y \times y) \times z \times(z x) \\ & =\left(x y^2 z\right) \times(z x) \\ & =(x \times x) \times y^2 \times(z \times z) \\ & =x^2 y^2 z^2\end{aligned}$
$\begin{aligned} \text { Required product } & =(x y) \times(y z) \times(z x) \\ & =x \times(y \times y) \times z \times(z x) \\ & =\left(x y^2 z\right) \times(z x) \\ & =(x \times x) \times y^2 \times(z \times z) \\ & =x^2 y^2 z^2\end{aligned}$
Question 142 Marks
Obtain the volume of rectangular boxes with the following length, breadth and height, respectively.
$2 p, 4 q, 8 r$
$2 p, 4 q, 8 r$
Answer
View full question & answer→We have, length $=2 p$, breadth $=4 q$ and height $=8 r$
$\therefore \text { Volume of rectangular box } $
$=\text { Length } \times \text { Breadth } \times \text { Height } $
$=(2 p) \times(4 q) \times(8 r) $
$=(2 \times 4 \times 8) \times(p \times q \times r) $
$ =64 p q r$
$\therefore \text { Volume of rectangular box } $
$=\text { Length } \times \text { Breadth } \times \text { Height } $
$=(2 p) \times(4 q) \times(8 r) $
$=(2 \times 4 \times 8) \times(p \times q \times r) $
$ =64 p q r$
Question 152 Marks
Complete the table of products.
| Ist monomial $\rightarrow$ | $2x$ | $-5y$ | $3 x^2$ | $-4 x y$ | $7 x^2 y$ | $-9 x^2 y^2$ |
| IInd monomial $\downarrow$ | ||||||
| $2x$ | $4 x^2$ | |||||
| $-5y$ | $-15 x^2 y$ | |||||
| $3 x^2$ | ||||||
| $-4 x y$ | ||||||
| $7 x^2 y$ | ||||||
| $-9 x^2 y^2$ |
Answer
View full question & answer→Here, to complete the table we will find the product of first monomial (in horizontal line) and second monomial (in vertical line) and write in corresponding place of table.
Question 162 Marks
Find the product of the following pairs of monomials.
(ii) $-4 p, 7 p$
(ii) $-4 p, 7 p$
Answer
View full question & answer→(ii) We have, $-4 p$ and $7 p$
$\begin{aligned}(-4 p) \times(7 p) & =[(-4) \times 7] \times(p \times p) \\& =(-28) \times p^2=-28 p^2\end{aligned}$
$\begin{aligned}(-4 p) \times(7 p) & =[(-4) \times 7] \times(p \times p) \\& =(-28) \times p^2=-28 p^2\end{aligned}$
Question 172 Marks
Simplify $(2 a+3 b)^2$.
Answer
View full question & answer→$\text {We have, }(2 \text{a}+3 b)^2=(2 \text{a})^2+(3 b)^2+2(2 \text{a} \times 3 b) $ $ \qquad[\because(\text{a}+\text{b})^2=\text{a}^2+2 \text{a} \text{b}+\text{b}^2] $
$ =2 \text{a} \times 2 \text{a}+2 \times 2 \text{a} \times 3 \text{b}+3 \text{b} \times 3 \text{b} $
$=4 \text{a}^2+12 \text{a} \text{b}+9 \text{b}^2$
$ =2 \text{a} \times 2 \text{a}+2 \times 2 \text{a} \times 3 \text{b}+3 \text{b} \times 3 \text{b} $
$=4 \text{a}^2+12 \text{a} \text{b}+9 \text{b}^2$
Question 182 Marks
Multiply $14 b, 3 a^2 b c$ and $16 c$.
Answer
View full question & answer→We have, $14 \text{b} \times 3 \text{a}^2 \text{b} \text{c} \times 16 \text{c}$ $=(14 \times 3 \times 16) \times \text{b} \times \text{b} \times \text{a}^2 \times \text{c} \times \text{c} $
$ =672 \times \text{b}^2 \times \text{a}^2 \times \text{c}^2 $
$=672\text{ b}^2 \text{ a}^2 \text{ c}^2$
$ =672 \times \text{b}^2 \times \text{a}^2 \times \text{c}^2 $
$=672\text{ b}^2 \text{ a}^2 \text{ c}^2$
Question 192 Marks
Subtract $7 p(3 q+7 p)$ from $8 p(2 p-7 q)$.
Answer
View full question & answer→We have, $8 p(2 p-7 q)=16 p^2-56 p q$
and $7 p(3 q+7 p)=21 p q+49 p^2$
$\therefore$ On subtracting, we get
and $7 p(3 q+7 p)=21 p q+49 p^2$
$\therefore$ On subtracting, we get