Factorization by Grouping Method

Q. Factorise
6(x+2y)³+8(x+2y)<sup>2

pls show steps</sup>

Q.

Factorise by splitting the middle term: 24^{x 2}- 65^x+ 21

1. (3^x - 7) ( 8^x + 3)

2. (3^x + 7) ( 8^x + 3)

3. (3^x - 7) ( 8^x - 3)

4. (3^x + 7) ( 8^x - 3)

Q. Factorise 4x^2+9y^2-12xy

Q. Factorise: 4(x-y)^2-12(x-y)+9

Q. $5xy+25y+3x+15$ is factorised as

1. $(5y+3)(x+5)$
2. $(y+3)(5x+25)$
3. $(y-3)(x-5)$

Q. Factorise Completely :
1) x²-y²-3x-3y
2) x²-y²-2x-2y

Q.

Factorise it :-

14(3y - 5z)³ + 7(3y - 5)²

Q. Which of the following represents the factorisation of $y^2+yz+9y+9z$?

1. $(9y+z)(y+9)$
2. $(y+9z)(y+9)$
3. $(y+z)(y+6)$
4. $(y+z)(y+9)$

Q. Factorisation of -xyx - x + 3xy + 3 gives:

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

Q. Factorise:
$4(x-y{)}^2-12(x-y\left)\right(x+y)+9(x+y{)}^2$
.........[3 marks]

Q. FACTORIZE:--
( i ) x²+ 8x + 15
( ii ) x² -- 23x + 132
( iii ) y²+ 5y -- 36
( iv ) y² + 2y -- 120
( v ) 4x² -- 12x + 5
( vi ) 6x² -- 13x+ 6
( vii ) p² + 15p + 56
( vii ) x² -- 11x -- 42

Q. Factorise: z-7+7xy-xyz

Q. $\text{Factorise:}12xy-8x+9y-6$

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

Q. The factorisation of 24xy + 8yz is

1. 24y(3x+z)
2. 3y(8x+z)
3. 8z(3x+y)
4. 8y(3x+z)

Q. Factorise:
i) y(y+z)+9(y+z)
ii) 10ab+4a+5b+2
iii) 6xy-4y+6-9x

Q. $\text{Factorise the given expression:}ab(x^2+y^2)+xy(a^2+b^2)$

1. $(bx+ay)(ax+by)$
2. $(b+a)(ax+by)$
3. $(ax+by)$
4. $(b{x}^2+a{y}^2)(ax+by)$

Q. $2pq+4pr-3sq-6sr$ = $(2p-3s)\times$

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

Q. Match the following algebraic expressions with their factorised form.

1. $x(3x+5)$
2. $(2x+6{)}^2$
3. $(x-4)(x+4)$
4. $5x(2x^3+6x^2+1)$

Q. factorise the following-
a2-7a+12

Q. One of the factors of $(a^2-b^2)(c^2-d^2)-4abcd$ is ______.

1. $(ac-bd+bc+ad)$
2. $(ac-bd+bc-ad)$
3. $(ac+bd+bc-ad)$
4. $(ac+bd+bc+ad)$

Q. $5xy+25y+3x+15$ is factorised as

1. $(5y+3)(x+5)$
2. $(y+3)(5x+25)$
3. $(y-3)(x-5)$

Q. Which of the following is the factorisation of (xy + x + 4y + 4)?

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

Q.

Which of the following is the factorised form of $20l^{2}m+30alm?$

1. $10lm(l+3a)$
2. $10lm(2l+3a)$
3. $5lm(2l+3a)$
4. $10lm(2l-3a)$

Q. Which of the following is the factorisation of (xy + x + 4y + 4)?

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

Q. Factorize: 3x^3+8x^2-1

Q.

Factorize the following expression:

$a(a-2b-c)+2bc$