Multiplication of a Monomial and a Polynomial

Q. Find the product of
$(a+b)\text{and}7a^2{b}^2.$

1. 7$a^2{b}^2$
2. $7a^3{b}^2+7a^2{b}^3$
3. $7a^{2}b+7a{b}^2$
4. $7ab+7a^2{b}^2$

Q.

Tick $\left(✓\right)$ the correct answer in each of the following:
$(2x+3)(3x-1)=?$

(a) $(6x^2+8x-3)$
(b) $(6x^2+7x-3)$
(c) $6x^2-7x-3$
(d) $(6x^2-7x+3)$

Q.

$x^4-(x-z{)}^4=$

1. $z(2x+z)(2x^2-2xz+z^2)$

2. $z(2x+z)(2x^2+2xz+z^2)$

3. $z(2x-z)(2x^2-2xz+z^2)$

4. $z(2x-z)(2x^2+2xz+z^2)$

Q. Find the product :
(i) (2x + 3y) (2x - 3y) $(4x^2+9y^2$)

Q.

The length of a rectangular field is one more than twice its breadth. Find its area if the breadth is $x$?

1. 2x - 1

2. 2 - x

3. + 2x

4. 2 + x

Q.

The length of a rectangular field is one more than twice the breadth. What is the area of this rectangular field, if the breadth is x?

1. 2x - 1

2. 2 + x

3. 2 - x

4. + 2x

Q.

Find each of the following products:
(i) $(x+3)(x-3)$
(ii) $(2x+5)(2x-5)$
(iii) $(8+x)(8-x)$
(iv) $(7x+11y)(7x-11y)$
(v) $(5x^2+\frac{3}{4}{y}^2)(5x^2-\frac{3}{4}{y}^2)$
(vi) $(\frac{4x}{5}-\frac{5y}{3})(\frac{4x}{5}+\frac{5y}{3})$
(vii) $(x+\frac{1}{x})(x-\frac{1}{x})$
(viii) $(\frac{1}{x}+\frac{1}{y})(\frac{1}{x}-\frac{1}{y})$
(ix) $(2a+\frac{3}{b})(2a-\frac{3}{b})$

Q.

Tick $\left(✓\right)$ the correct answer in each of the following:

$(x+5)(x-3)=?$

(a) $x^2+5x-15$
(b) $x^2-3x-15$
(c) $x^2+2x+15$
(d) $x^2+2x-15$

Q.

Find each of the following products:
(i) $(x+6)(x+6)$
(ii) $(4x+5y)(4x+5y)$
(iii) $(7a+9b)(7a+9b)$
(iv) $(\frac{2}{3}x+\frac{4}{5}y)(\frac{2}{3}x+\frac{4}{5}y)$
(v) $(x^2+7)(x^2+7)$
(vi) $(\frac{5}{6}{a}^2+2)(\frac{5}{6}{a}^2+2)$

Q. The expression $a^3+b^3+c^3-3abc$ can be expressed as a product of two expressions. What is the product?

1. $(a-b-c)(a^2+b^2+c^2-ab-bc-ca)$
2. $(a+b+c)(a^2-b^2-c^2-ab-bc-ca)$
3. $(a+b+c)(a^2+b^2+c^2+ab+bc+ca)$
4. $(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$

Q.

What has to be added to $x^2+3x-8$ to get $x^2+x+6$?

1. 3 - 8

2. - 2x + 14

3. x + 6

4. 2x + 14

Q. Simplify $-15(-x^{2}y{z}^2+2p{q}^2-3mn)$

1. $15(x^{2}y{z}^2-2p{q}^2+3mn)$
2. $15(x^{2}yz+2p{q}^2-3mn)$
3. $15x^{2}y{z}^2+30p{q}^2+45mn$
4. $15x^{2}y{z}^2-30p{q}^2-45mn$

Q. Question 11

Volume of a rectangular box (cuboid) with length = 2ab, breadth = 3ac and height = 2ac is
a) $12a^{3}b{c}^2$
b) $12a^{3}bc$
c) $12a^{2}bc$
d) $2ab+3ac+2ac$

Q. The number of terms that you get on simplifying (3x + 5)(x - 4) is

1. 2
2. 3
3. 4
4. 5

Q. The product of 4xy and 4x + 3y is $16x^{2}y+12x{y}^2$.

1. True
2. False

Q.

The volume of rectangular box having length, breadth and height as $(a+b),(a^2+b^2)and2a$ respectively is $2a^4+2a^2{b}^2+2a^{3}b+2a{b}^3$

1. True

2. False

Q. Write the given expression in the product form.
$30x^4{y}^4{z}^5$.

Q. $8x{y}^2$ is one of the terms of the resulting expression when we multiply $2x{y}^2$ and $4xy+2$.

1. True
2. False

Q. Give possible expression for the length and breadth of the rectangle whose area is : $4a^2+4a-3$

1. $(2a-3)(2a+2)$
2. $(2a-1)(2a-3)$
3. $(2a+3)(2a-1)$
4. None of the above

Q.

The length of a rectangular field is one more than twice of the breadth. What is its area if the breadth is $x$?

1. $2x-1$

2. 2$x^2$ - $x$

3. $x^2$ + $2x$

4. 2$x^2$ + $x$

Q. The product of $(a+b)$ and 7$a^2$$b^2$ is .

1. 7$a^2{b}^2$
2. $7a^3{b}^2+7a^2{b}^3$
3. $7a^{2}b+7a{b}^2$
4. $7ab+7a^2{b}^2$

Q. Find the area of the shaded portion.

1. $210m^2$
   
2. $250m^2$
   
3. $220m^2$
   
4. $240m^2$
   

Q. If $g\left(x\right)=x^2+x-2$, which of the following is true?

1. $g\left(x\right)$ is even.
2. $[-g(x\left)\right]=g\left(x\right)$
3. $g\left(x\right)$ is neither even nor odd.
4. $g\left(x\right)$ is odd.

Q. Multiply $2x$, $\frac{5y}{2}$ and $z^2$

1. $5xy{z}^2$
2. $2xy{z}^2$
3. $5x{y}^{2}z$
4. none of these

Q.

Find the product of $(x+y-z+p)$ and $xyzp$.

1. $x^{2}yzp+x{y}^{2}zp+xy{z}^{2}p+xyz{p}^2$

2. $2xyzp-xy{z}^{2}p+xyz{p}^2$

3. $2xyzp+xy{z}^{2}p+xyz{p}^2$

4. $x^{2}yzp+x{y}^{2}zp-xy{z}^{2}p+xyz{p}^2$

Q. $8x{y}^2$ is one of the terms of the resulting expression when we multiply $2x{y}^2$ and $4xy+2$.

1. True
2. False

Q.

$(a+b+c)(a-b-c)$ = ______

1. $a^2+b^2+c^2-bc$

2. $a^2+b^2-c^2-ca$

3. $a^2-b^2+c^2-2ca$

4. $a^2-b^2-c^2-2bc$

Q.

What is the product of $(a+b)$ and $7a^2$$b^2$?

1. 7

2. 7 + 7

3. 7b + 7a

4. 7ab + 7