Algebraic Expressions and Identities Test

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Algebraic Expressions and Identities Test - 37

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Weekly Quiz Competition

Question 1
1 / -0

The product of $$4{ a }^{ 2 }$$, $$-6{ b }^{ 2 }$$ and $$3{ a }^{ 2 }{ b }^{ 2 }$$ is

A
$${ a }^{ 2 }{ b }^{ 2 }$$

B
$$13{ a }^{ 4 }{ b }^{ 4 }$$

C
$$-72{ a }^{ 4 }{ b }^{ 4 }$$

D
$${ a }^{ 4 }{ b }^{ 4 }$$

Solution

$$4a^{2}\times (-6b^{2})\times 3a^{2}b^{2}$$
$$=4\times a\times a\times -6\times b\times b\times 3\times a\times a\times b\times b$$
$$=4\times -6\times 3\times a\times a\times a\times a\times b\times b\times b\times b$$
$$=-72 a^{4}b^{4}$$
Question 2
1 / -0

The value of the product $$\left( 4{ a }^{ 2 }+3b \right) \left( 9{ b }^{ 2 }+4a \right) $$ at $$a=1$$, $$b=-2$$ is

A
$$60$$

B
$$-80$$

C
$$70$$

D
$$-50$$

Solution

$$(4a^{2}+3b)(9b^{2}+4a)$$
$$=36a^{2}b^{2}+27b^{3}+16a^{3}+12ab$$

Put the value of $$a=1$$ and $$b=-2$$, we get
$$(4a^{2}+3b)(9b^{2}+4a)\\$$
$$=36\times (1)^{2}\times (-2)^{2}+27\times (-2)^{3}+16\times (1)^{3}+12\times (1)\times (-2)\\$$
$$=36\times 4-27\times 8+16\times 1-12\times 2\\$$
$$=144-216+16-24=-80$$
Question 3
1 / -0

The expression $$\displaystyle -8{ x }^{ 3 }\left( 7{ x }^{ 6 }-3{ x }^{ 5 } \right) $$ equals:

A
$$\displaystyle -56{ x }^{ 9 }+24{ x }^{ 8 }$$

B
$$\displaystyle -56{ x }^{ 9 }-24{ x }^{ 8 }$$

C
$$\displaystyle -56{ x }^{ 18 }+24{ x }^{ 15 }$$

D
$$\displaystyle -56{ x }^{ 18 }-24{ x }^{ 15 }$$

E
$$\displaystyle -32{ x }^{ 4 }$$

Solution

The expression equals $$-8x^3(7x^6-3x^5)$$
$$\Rightarrow -56x^{3+6}+24x^{3+5}$$
$$\Rightarrow -56x^9+24x^8$$
Question 4
1 / -0

The product of the monomials $$\displaystyle \left( 2{ x }^{ 4 }y \right)$$ and $$\left( 3{ x }^{ 5 }{ y }^{ 8 } \right) $$ is :

A
$$\displaystyle 5{ x }^{ 9 }{ y }^{ 9 }$$

B
$$\displaystyle 6{ x }^{ 9 }{ y }^{ 8 }$$

C
$$\displaystyle 6{ x }^{ 9 }{ y }^{ 9 }$$

D
$$\displaystyle 5{ x }^{ 20 }{ y }^{ 8 }$$

E
$$\displaystyle 6{ x }^{ 20 }{ y }^{ 8 }$$

Solution

The product of monomials $$2x^4y$$ and $$3x^5y^8$$ is
$$ 2x^4y\times 3x^5y^8= 2(3).x^4(x^5).y^1(y^8)$$
$$\Rightarrow 6x^{4+5}y^{1+8}$$
$$\Rightarrow 6x^9y^9$$
Question 5
1 / -0

Number of terms in the expansion $$\left( a+b \right) \left( c+d \right) $$ is ________.

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

given, $$(a+b)(c+d)$$

$$=ac+bc+ad+bd$$

In above expression the number of terms are Four (4)
Question 6
1 / -0

Expand the expression $$4(5x+3)(2x-1)$$.

A
$$40x^2+12$$

B
$$40x^2-12$$

C
$$40x^2+4x+12$$

D
$$40x^2+4x-12$$

Solution

On expanding, we get
$$ 4(5x+3)(2x-1)$$
$$\Rightarrow 4(10x^2+6x-5x-3)$$
$$\Rightarrow 4(10x^2+x-3)$$
$$\Rightarrow 40x^2+4x-12$$
Question 7
1 / -0

Multiply the binomials $$\displaystyle \left( 4z+3 \right) $$ and $$\left( z-2 \right) $$ :

A
$$\displaystyle 4{ z }^{ 2 }-5$$

B
$$\displaystyle 4{ z }^{ 2 }-6$$

C
$$\displaystyle 4{ z }^{ 2 }-3z-5$$

D
$$\displaystyle 4{ z }^{ 2 }-5z-6$$

E
$$\displaystyle 4{ z }^{ 2 }+5z-6$$

Solution

On multiplying, $$(4z+3)(z-2)$$
$$\Rightarrow 4z(z-2)+3(z-2)$$
$$\Rightarrow 4z^2-8z+3z-6$$
$$\Rightarrow 4z^2-5z-6$$
Question 8
1 / -0

Find the product of $$(15x-11)$$ and $$(6-5x)$$.

A
$$-75x^2-35x-66$$

B
$$-75x^2+145x-66$$

C
$$90x^2-141x+55$$

D
$$90x^2-9x+55$$

Solution

The product of $$(15x - 11) \times (6 - 5x)$$
$$= 15x(6 - 5x) - 11(6 - 5x)$$
$$= 90x - 75x^2 - 66 + 55x$$
$$= -75x^2 + 145x - 66$$
Question 9
1 / -0

$$-4p\left( 3q-5p \right) =$$

A
$$-12pq-20{ p }^{ 2 }$$

B
$$-12pq+20{ p }^{ 2 }$$

C
$$-7pq+20{ p }^{ 2 }$$

D
$$-7pq-20{ p }^{ 2 }$$

Solution

Multiplying $$-4p$$ with $$(3q-5p)$$
$$-4p(3q) = -12pq$$ $$-4p(-5p)$$
$$= -12pq+20p^2$$
Question 10
1 / -0

What is the product $$(x + 2)(x - 3)$$?

A
$$2x-6$$

B
$$3x-2$$

C
$$x^2-x-6$$

D
$$x^2-6x$$

Solution

$$(x+a)(x+b)$$ $$=$$$$x^2+(a+b)x+ab$$
In this formula, taking $$x=x$$ $$a= 2$$ $$b= (-3)$$
$$(x+2)(x-3)$$ = $$x^2+[(2+ (-3)]x+2(-3)$$
$$\Rightarrow$$ $$x^2-1x-6$$
$$\Rightarrow$$ $$\boxed{x^2-x-6}$$

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Re-Attempt Weekly Quiz Competition

Algebraic Expressions and Identities Test - 37

Result

Algebraic Expressions and Identities Test - 37

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SHARING IS CARING

Question 1

$${ a }^{ 2 }{ b }^{ 2 }$$

$$13{ a }^{ 4 }{ b }^{ 4 }$$

$$-72{ a }^{ 4 }{ b }^{ 4 }$$

$${ a }^{ 4 }{ b }^{ 4 }$$

Solution

Question 2

$$60$$

$$-80$$

$$70$$

$$-50$$

Solution

Question 3

$$\displaystyle -56{ x }^{ 9 }+24{ x }^{ 8 }$$

$$\displaystyle -56{ x }^{ 9 }-24{ x }^{ 8 }$$

$$\displaystyle -56{ x }^{ 18 }+24{ x }^{ 15 }$$

$$\displaystyle -56{ x }^{ 18 }-24{ x }^{ 15 }$$

$$\displaystyle -32{ x }^{ 4 }$$

Solution

Question 4

$$\displaystyle 5{ x }^{ 9 }{ y }^{ 9 }$$

$$\displaystyle 6{ x }^{ 9 }{ y }^{ 8 }$$

$$\displaystyle 6{ x }^{ 9 }{ y }^{ 9 }$$

$$\displaystyle 5{ x }^{ 20 }{ y }^{ 8 }$$

$$\displaystyle 6{ x }^{ 20 }{ y }^{ 8 }$$

Solution

Question 5

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 6

$$40x^2+12$$

$$40x^2-12$$

$$40x^2+4x+12$$

$$40x^2+4x-12$$

Solution

Question 7

$$\displaystyle 4{ z }^{ 2 }-5$$

$$\displaystyle 4{ z }^{ 2 }-6$$

$$\displaystyle 4{ z }^{ 2 }-3z-5$$

$$\displaystyle 4{ z }^{ 2 }-5z-6$$

$$\displaystyle 4{ z }^{ 2 }+5z-6$$

Solution

Question 8

$$-75x^2-35x-66$$

$$-75x^2+145x-66$$

$$90x^2-141x+55$$

$$90x^2-9x+55$$

Solution

Question 9

$$-12pq-20{ p }^{ 2 }$$

$$-12pq+20{ p }^{ 2 }$$

$$-7pq+20{ p }^{ 2 }$$

$$-7pq-20{ p }^{ 2 }$$

Solution

Question 10

$$2x-6$$

$$3x-2$$

$$x^2-x-6$$

$$x^2-6x$$

Solution

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