(a ± b)²

Q.

Factorize $a^3+b^3+c^3-3abc$.

Q.

What are the $4$ methods of factoring ?

Q.

Factorise:

$(x^2+\frac{1}{x^2})-4(x+\frac{1}{x})+6$

Q.

Factorize:

$2a^2+2\sqrt{6}ab+3b^2$

Q.

Factorize:

$x{y}^9-y{x}^9$

Q.

Factorize:

$4(x-y{)}^2+12(x-y\left)\right(x+y)+9(x+y{)}^2$

Q.

Factorize:

$a^2+b^2+2(ab+bc+ca)$

Q.

Factorize:

$(x+2)(x^2+25)-10x^2-20x$

Q.

Factorise the following: $27-125a^3-135a+225a^2$

Q.

Factorise the following expression: ${\left(l+m\right)}^2-4lm$

Q. Factorize: $a^2+2+\frac{1}{a^2}$

1. $(a-\frac{1}{a}{)}^2$
2. $(a+\frac{1}{a}{)}^2$
3. $(a+\frac{2}{a}{)}^2$
4. $(-a+\frac{1}{a}{)}^2$

Q. Factorise $(1-x^2)(1-y^2)+4xy$ is _____

1. $(1+yx+x+y)(1+xy-x+y)$
2. $=(1+yx+x-y)(1+xy-x-y)$
3. $=(1+yx+x-y)(1+xy-x^2-y^2)$
4. $=(1-y^{2}x+x-y)(1+xy-x-y)$

Q.

Factorise: $(p^2+q^2-r^2{)}^2-4p^2{q}^2$

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

Q. Factorise $a^4-16$ is ____

1. $(a-2)(a+2)(a^2+4)$
2. $(a+11)(2a+12)(a^2-12)$
3. $(a^2-2)(a+2)(a^2+2)$
4. $(a^2-2)(a^2+2)(a^2+2)$

Q.

Factorize:

$x^4+x^2{y}^2+y^4$

Q. Factorize: $a^2-14a+49$

1. $(a-7)(a+7)$
2. $(a+7{)}^2$
3. $(a-7{)}^2$
4. $(a-49)(a+7)$

Q.

Factorization of $64a^3–343b^3$ is:

1. (4a – 7b) (16a² + 49b² + 28ab)

2. (4a + 7b) (16a² - 49b² + 28ab)

3. (4a – 7b) (16a² + 49b² - 28ab)

4. (4a + 7b) (16a² + 49b² + 28ab)

Q. Factorise $100-x^2$

1. $x^2+2x+50$
2. $(x+20)(x-5)$
3. $(x+10)(10-x)$
4. $x^3-12x+50$

Q. Match the following expressions with their factorised form.

1. $(x+4)(x-4)$
2. $(x+1{)}^2$
3. $(x-6{)}^2$
4. $(x-7)(x+7)$

Q. Factorise $a^2-(2a+3b{)}^2$ is _____.

1. $(2a+5b)(7a+3b)$
2. $-2a(a+b^2)(a^2+3b)$
3. $-a(a+b)(a+3b)$
4. $-6a(8a+b)(3a+b^2)$

Q. Factorise $x(x-a)-y(y-a)$

1. $(x+y)(x+y-a)$
2. $(x-y)(x+y)$
3. $(x+y)(x-y-a)$
4. $(x-y)(x+y-a)$

Q.

Factorise:

$a^2+4b^2-4ab-4c^2$

Q.

The factorization of $x^3+1$ is

1. (x+1)(x²+x+1)

2. (x+1)(x²-x+1)

3. (x-1)(x²-x+1)

4. (x+1)(x²+x-1)

Q. Let $S_n=\sum _{k=1}^{4n}(-1)\frac{k(k+1)}{2}{k}^2$ . Then $S_n$ can take value (s)

1. $16n^2+4n.$
2. $18n^2+4n.$
3. $16n^2+3n.$
4. $16n^2+5n.$

Q.

Factorize the following: $27p^3-\frac{1}{216}-\frac{9}{2}{p}^2+\frac{1}{4}p$

Q.

Factorise:

$(a-b+c{)}^2+(b-c+a{)}^2+2(a-b+c)(a-c+a)$

Q. Factorise:$(x^2+4y^2-9z^2{)}^2-16x^2{y}^2$

1. $(x^2+y^2-9z^2-4xy)(x^2+y^2-9z^2+4xy)$
2. $(x^2-y^2-9z^2-4xy)(x^2-y^2-9z^2+4xy)$
3. $(x^2+y^2-9z^2+4xy{)}^2$
4. $(x^2-y^2-9z^2-4xy{)}^2$

Q. The expression $a^2+b-ab-a$ can be factorise as

1. $(a-b)(a+1)$
2. $(a+b)(a-1)$
3. $(a-b)(a-1)$
4. $(a+b)(a+1)$

Q. Factorise : $4a^2-9b-2bc-c^2$

Q. Factorize: $(3x-2y{)}^2+3(3x-2y)-10$

1. $(3x+2y-5)(3x-2y+2)$
2. $(3x-2y+5)(3x-2y-2)$
3. $(3x+2y+5)(3x+2y-2)$
4. $(3x-2y-5)(3x-2y-2)$