Visualisation of Factorisation

Q. Evaluate :
(i) $(2x+3y{)}^2$ (ii) $(2x-3y{)}^2$ (iii) $(2x+3y)(2x-3y)$

Q. Factorise $81x^2-49y^2$.

1. (9x - 7y)(9x + 7y)
2. (9x + 7y)(9x + 7y)
3. (9x - 7y)(9x - 7y)
4. (3x - 7y)(3x + 7y)

Q. Factorise $x^2-6x+9$

1. (x + 3)(x - 3)
2. (x - 3)(x - 3)
3. (x + 3)(x + 3)
4. (x + 3)(x - 2)

Q.

Evaluate the following products without multiplying directly:
$95\times 96$

1. 4860

2. 9210

3. 4680

4. 9120

Q. Evaluate:
(i) $(4x+2y{)}^2$
(ii) $(5x-y{)}^2$
(iii) $(3x+7y)(3x-7y)$

Q. Which of the following is a factor of $a^2{x}^3-2ab{x}^2+b^{2}x$?

Q. $a^2-b^2=(a+b)(a-b)$ can be used to factorise the expression $36x^2-25$.

1. False
2. True

Q.

If $A+B=5$ and $AB=6$. Find $A^3+B^3$.

1. 125

2. 90

3. 215

4. 35

Q. $(a+b{)}^2$ expands as $a^2+b^2+2ab$.

1. True
2. False

Q. $x^2+5x+6=$

1. $(x+3)(x+5)$
2. $(x+5{)}^2$
3. $(x+3)(x+2)$

Q. $\frac{(x^2-b)(x-a)}{(a-x)}$ =

1. $(b^2-x^2)$
2. $(x^2-b)$
3. $(b+x^2)$
4. $(b-x^2)$

Q. $(2x-3{)}^2=4x^2-6x+9$

1. True
2. False

Q. Match the following expressions using suitable identities.

1. $(m-4{)}^2$
2. $(m+2)(m+7)$
3. $(3m+2)(3m-2)$

Q. Factorise the following :
$x^2+2xy-99y^2$

Q. Which of the following can be solved using algebraic identities?

1. $4+6$
2. $(5+3{)}^2$
3. $(15-10{)}^2$
4. $12-4$
5. $4^2-3^2$
6. $6-4\times 6+4$
7. $6+3\times 6+4$
8. $5-2\times 7+3$