Application of Algebraic Identities

Q. If $a+b=25$ and $a^2+b^2=225$, then find ab.

1. 180
2. 204
3. 214
4. 200

Q.

Question 1(vi)
Multiply the binomials:
$(\frac{3}{4}{a}^2+3b^2)and4(a^2-\frac{2}{3}{b}^2)$

Q. Using an identity, find the value of
${12.1}^2-{7.9}^2.$

1. 80
2. 84
3. 88
4. 86

Q.

Find the value of $1010\times 990$ , using identities.

1. 999900

2. 100000
3. 990000
4. 119900

Q. Simplify: (0.8m + 1.1n) (0.8m - 1.1n)

1. $0.64m^2+1.12n^2$
2. $0.64m^2+1.21n^2$
3. $0.64m^2-1.21n^2$
4. $0.64m^2-11.2n^2$

Q. Which of the following identities can be used to solve 1001 $\times$ 999?

1. $(a+b)\times (a-b)=a^2-b^2$
2. ${(a+b)}^2=a^2+2ab+b^2$
3. ${(a-b)}^2=a^2-2ab+b^2$
4. None of the above

Q.

The value of $(a+1)(a-1)(a^2+1)$ is $a^4-1$.

1. True

2. False

Q.

${(4pq+3q)}^2-{(4pq-3q)}^2=$ ____________.

1. $48p^{2}q$

2. $44p^{2}q$

3. $48p{q}^2$

4. $44p{q}^2$

Q.

$\text{If}{x}^2+y^2=14\text{and}xy=3,$
then find the value of
$2(x+y{)}^2-5(x-y{)}^2.$

1. 0

2. 106

3. 14

4. 52

Q.

If $(x^2-y^2)=18$ and $(x-y)=3$, find the value of $x^2+y^2+2xy$.

1. 81

2. 243

3. 729

4. 27

Q. If $x+y=7$ and $xy=12$, find $x^2+y^2$.

Q.

Lowest form of $\frac{x^4+x^{3}y+x^2{y}^2}{x^3-y^3}$

1. $\frac{x^3}{(x-y)}$

2. $\frac{x^2}{(x+y)}$

3. $\frac{x^2}{(x-y)}$

4. $\frac{x^2+y}{(x+y^2)}$

Q.

Find the product.

(i) $a^2\times \left(2a^{22}\right)\times \left(4a^{26}\right)$

Q.

Simplify:
$[{(5z-2)}^2+40z]÷(5z+2)$

1. $2z+5$

2. $2z-5$

3. $5z-2$

4. $5z+2$

Q. Evaluate by using suitable identity : ${997}^3$

Q. $(q+p)\times (q-p)$ = ___________.

1. $p^2$ + $q^2$
2. $p^2$ - $q^2$
3. $q^2$ - $p^2$
4. ${(q-p)}^2$

Q.

The product ( $y$ + $\frac{1}{y}$ ) ( $y$ - $\frac{1}{y}$ ) can be simplified as _______.

1. 2 $y$

2. $y^2$ + $\frac{1}{y^2}$

3. 2 $y^2$

4. $y^2$ - $\frac{1}{y^2}$

Q.

Simplify $(xy+yz{)}^2-2x^2{y}^{2}z$ and find it's value when $x=-1,y=1$ and $z=2$.

1. 3

2. 4

3. -3

4. 0

Q. If${(6x+3y)}^2$= 576 and xy=6, find the value of $36x^{2}9y^2$

Q. The value of ${(4pq+3q)}^2-{(4pq-3q)}^2=$.

1. $48p{q}^2$
2. $42p{q}^2$
3. $48p^{2}q$

Q.

The value of $(109{)}^2$ is _______.

1. 10881

2. 11881

3. 11891

4. 11880

Q.

Evaluate : ( 5 $x$ +4$y$ ) (5$x$ -4$y$ )

1. 25$x^2$ +16$y^2$

2. 25$x^2$ -16$y^2$

3. 25$x^2$ -4$y^2$

4. 5$x^2$ -16$y^2$

Q. State whether the statement is True or False:

1. True
2. False

Q. Show that :

$\left(i\right){(3x+7)}^2-84x={(3x-7)}^2$

$\left(ii\right){(4pq+3q)}^2-{(4pq-3q)}^2=48p{q}^2$

$\left(iii\right)(a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)=0$

Q.

Reduce to the lowest form of: $\frac{2}{x-1}$+$\frac{3}{x+1}$ =

1. $\frac{(5x-1)}{(x-1)}$

2. $\frac{\left(1\right)}{(x^2-1)}$

3. $\frac{(6x+1)}{(x^2-1)}$

4. $\frac{(5x-1)}{(x^2-1)}$

Q. The value of ${(4pq+3q)}^2-{(4pq-3q)}^2=$.

1. $48p{q}^2$
2. $42p{q}^2$
3. $48p^{2}q$

Q.

${(4pq+3q)}^2-{(4pq-3q)}^2=$ ____________.

1. 44p

2. 48q

3. 48pq²

4. 44q

Q. $(4x^3+2x^2+4x+4)\times 2$

1. $4x^2+8x+10$
2. $8x^3+4x^2+8x+8$
3. $8x^3+4x^2+8x+10$
4. None of the above

Q.

Which of the following is not true?

1. ${(a-b)}^2$ = $a^2$ - 2ab + $b^2$

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

3. ${(a+b)}^2$ = $a^2$ - 2ab + $b^2$

4. ${(a+b)}^2=b^2$ + 2ab + $a^2$

Q.

Show that :

$\left(i\right){(3x+7)}^2-84x={(3x-7)}^2$

$\left(ii\right){(4pq+3q)}^2-{(4pq-3q)}^2=48p{q}^2$

$\left(iii\right)(a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)=0$ [3 MARKS]