Algebraic Expressions and Identities Test

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Algebraic Expressions and Identities Test - 31

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Weekly Quiz Competition

Question 1
1 / -0

Using $$(x + a) (x + b) = x^2+(a+b)x+ab$$, find $$5.1 \times 5.2$$.

A
$$17.61$$

B
$$22.41$$

C
$$13.32$$

D
$$26.52$$

Solution

Given,
$$5.1 \times 5.2 = (5 + 0.1)(5 + 0.2)$$.

We know, $$ (x+a)(x+b)=x^2+(a+b)x+ab$$.

Then,
$$5.1 \times 5.2 $$
$$= (5 + 0.1)(5 + 0.2)$$
$$ = (5)^2 + (0.1 + 0.2) (5)+ (0.1)(0.2)$$
$$ = 25 + (0.3) (5)+ 0.02$$
$$=25 + 1.5 + 0.02$$
$$= 26.52$$.

Therefore, option $$D$$ is correct.
Question 2
1 / -0

The value of $$(x + 3y)^2 + (x - 3y)^2$$ is:

A
$$2x^2 + 18 y^2$$

B
$$2x^2 - 18 y^2$$

C
$$2x^2 + 18y^2 - 2xy$$

D
None of these

Solution

We know, $$(a+b)^2=a^2+2ab+b^2$$ and $$(a-b)^2=a^2-2ab+b^2$$.

Then,
$$(x + 3y)^2 + (x - 3y)^2=[(x)^2+(3y)^2+2\times x\times3y]+[(x)^2+(3y)^2-2\times x\times3y]$$
$$=x^2+9y^2+6xy+x^2+9y^2-6xy$$
$$=2x^2+18y^2$$.

Hence, Option $$A$$ is correct.
Question 3
1 / -0

If $$(3x -4) (5x+7)= 15x^2-ax-28$$ then $$a =$$____

A
1

B
-1

C
-2

D
none of these

Solution

Hence,
$$(3x -4) (5x+7)= 15x^2-ax-28$$
$$\Rightarrow15x^2+21x-20x-28=15x^2-ax-28$$
$$\Rightarrow15x^2+x-28=15x^2-ax-28$$
Equating the terms having similar powers:-
$$\Rightarrow x=-ax$$
$$\Rightarrow a=-1$$
$$\Rightarrow$$ Option B is correct.
Question 4
1 / -0

Simplify: $$(x + 5)(x + 4)$$

A
$$x^2+27x+20$$

B
$$x^2+9x+20$$

C
$$x^2+18x+20$$

D
$$x^2+x+20$$

Solution

$$(x + 5)(x + 4)$$, using the formula $$(x+a)(x+b)=x^2+x(a+b)+ab$$
$$=x^2+x(5+4)+5\times 4$$
$$=x^2+9x+20$$
Question 5
1 / -0

$$(x + 2)(x + 3) -(x + 3)(x -2)=$$

A
12

B
0

C
6x

D
4x+12

Solution

$$\textbf{Step 1: Multiply the factors by distribution law}$$
$$(x+2)(x+3)-(x+3)(x-2)$$
  $$\Rightarrow x(x+3)+2(x+3)-(x(x-2)+3(x-2))$$
  $$\Rightarrow x^2+3x+2x+6-(x^2-2x+3x-6)$$
  $$\Rightarrow x^2+3x+2x+6-x^2+2x-3x+6$$ $$\text{[multiplying with $$(-)$$ will change the sign]}$$
  $$\Rightarrow x^2+5x+6-x^2-x+6$$
  $$\Rightarrow 4x+12$$

$$\textbf{Hence, Option D is correct}$$
Question 6
1 / -0

$$(4x + 1)\times (4x + 1) =$$

A
$$16x^{2} + 8x + 2$$

B
$$16x^{2} + 8x + 1$$

C
$$16x^{2} + 8x + 3$$

D
None of the above

Solution

Given that: $$ (4x+1)\times(4x+1)$$
No we can see that: $$ (4x+1)\times(4x+1) =$$ $$ 4x\times(4x+1)+1\times (4x+1)$$
$$\Rightarrow (4x\times 4x)+(4x\times 1)+(1\times 4x)+(1\times 1)$$
$$\Rightarrow 16x^2+4x+4x+1$$
$$\Rightarrow 16x^2+8x+1$$
Question 7
1 / -0

Find the product of $$\left( 3x-5 \right)$$ and $$\left( x+5 \right) $$.

A
$${ x }^{ 2 }-25x+10$$

B
$${ x }^{ 2 }+10x-22$$

C
$$3{ x }^{ 2 }+10x-25$$

D
$$3{ x }^{ 2 }-22x-25$$

Solution

Product of $$(3x-5)(x+5)=3x(x+5)-5(x+5)$$
$$=3x^2+15x-5x-25$$
$$=3x^2+10x-25$$
Option C is correct.
Question 8
1 / -0

$$(a -b)^2 -(a + b)^2$$ is equal to:

A
$$2ab$$

B
$$4ab$$

C
$$6ab$$

D
$$-4ab$$

Solution

Given, $$(a -b)^2-(a + b)^2 $$.

We know, $$(x+y)^2=x^2+2xy+y^2$$
and $$(x-y)^2=x^2-2xy+y^2$$.

Then,
$$(a -b)^2-(a + b)^2 $$
$$= (a^2 + b^2 -2ab) -(a^2 + b^2 + 2ab) $$
$$= a^2 + b^2 -2ab -a^2 - b^2 - 2ab) $$
$$= -4ab$$.

Therefore, option $$D$$ is correct.
Question 9
1 / -0

The product of a monomial and a trinomial is a

A
monomial

B
binomial

C
trinomial

D
none of these

Solution

The product of a monomial and trinomial results trinomial.

For example: Suppose a monomial $$2x$$ and a trinomial $$2x+3y+3$$.

Their product will be $$2x(2x+3y+3)=4x^2+6xy+6x$$

The result is a trinomial.

Hence, option C is correct.
Question 10
1 / -0

$$(3x+2y)(x+y)$$

A
$$3x^2+y^2+5xy$$

B
$$3x^2+2y^2+5xy$$

C
$$3x^2+2y^2+6xy$$

D
$$3x^2+2y+5xy$$

Solution

$$=(3x+2y)(x+y)$$
$$=3x\times x+2y\times y+3x\times y+2y\times x$$
$$= 3x^2+2y^2+5xy$$

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Algebraic Expressions and Identities Test - 31

Result

Algebraic Expressions and Identities Test - 31

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SHARING IS CARING

Question 1

$$17.61$$

$$22.41$$

$$13.32$$

$$26.52$$

Solution

Question 2

$$2x^2 + 18 y^2$$

$$2x^2 - 18 y^2$$

$$2x^2 + 18y^2 - 2xy$$

None of these

Solution

Question 3

1

-1

-2

none of these

Solution

Question 4

$$x^2+27x+20$$

$$x^2+9x+20$$

$$x^2+18x+20$$

$$x^2+x+20$$

Solution

Question 5

12

0

6x

4x+12

Solution

Question 6

$$16x^{2} + 8x + 2$$

$$16x^{2} + 8x + 1$$

$$16x^{2} + 8x + 3$$

None of the above

Solution

Question 7

$${ x }^{ 2 }-25x+10$$

$${ x }^{ 2 }+10x-22$$

$$3{ x }^{ 2 }+10x-25$$

$$3{ x }^{ 2 }-22x-25$$

Solution

Question 8

$$2ab$$

$$4ab$$

$$6ab$$

$$-4ab$$

Solution

Question 9

monomial

binomial

trinomial

none of these

Solution

Question 10

$$3x^2+y^2+5xy$$

$$3x^2+2y^2+5xy$$

$$3x^2+2y^2+6xy$$

$$3x^2+2y+5xy$$

Solution

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