Question

m(x-3y)^2+n(3y-x)+5x-15y factorise with grouping method

Answer 1

1. Factor grouping the expressions:

` 


1 + a + ac + a2c 

Solution: 

1 + a + ac + a2c 

= (1 + a) + (ac + a2c)

= (1 + a) + ac (1 + a) 

= (1 + a) (1 + ac). 


2. How to factor by grouping the following algebraic expressions?


(i) a2 - ac + ab - bc

Solution: 

a2 - ac + ab - bc

= a(a - c) + b(a - c)

= (a - c) (a + b)

Therefore, by factoring expressions we get (a - c)(a + b)


(ii) a2 + 3a + ac + 3c


Solution: 

a2 + 3a + ac + 3c

= a(a + 3) + c(a + 3)

= (a + 3) (a + c)

Therefore, by factoring expressions we get (a + 3)(a + c)


3. Factorize the algebraic expressions:


(i) 2x + cx + 2c + c2

Solution: 

2x + cx + 2c + c2

= x(2 + c) + c(2 + c)

= (2 + c) (x + c)


(ii) x2 - ax + 5x - 5a

Solution: 

x2 - ax + 5x - 5a

= x(x - a) + 5(x - a)

= (x - a) (x + 5)

`

(iii) ax - bx - az + bz

Solution: 

ax - bx - az + bz

= x(a - b) - z(a - b)

= (a - b) (x - z)

(iv) mx - 2my - nx + 2ny

Solution: 

mx - 2my - nx + 2ny

= m(x - 2y) - n(x - 2y) 

= (x - 2y) (m - n) 


(v) ax2 - 3bxy – axy + 3by2 

Solution: 

ax2 - 3bxy – axy + 3by2

= x(ax – 3by) – y(ax – 3by) 

= (ax - 3by) (ax - y) 

4. Factor each of the following expressions by grouping:


(i) x2 - 3x - xy + 3y

Solution: 

x2 - 3x - xy + 3y

= x(x – 3) – y(x – 3) 

= (x – 3) (x – y) 


(ii) ax2 + bx2 + 2a + 2b

Solution: 

ax2 + bx2 + 2a + 2b

= x2(a + b) + 2(a + b) 

= (a + b) (x2 + 2) 

(iii) 2ax2 + 3axy - 2bxy - 3by2 

Solution: 

2ax2 + 3axy - 2bxy - 3by2

= ax(2x + 3y) - by(2x + 3y) 

= (2x + 3y) (ax - by) 


(iv) amx2 + bmxy – anxy – bny2

Solution: 

amx2 + bmxy – anxy – bny2

= mx(ax + by) – ny(ax + by) 

= (ax + by) (mx – ny) 


5. Factorize:

(i) (x + y) (2x + 5) - (x + y) (x + 3) 

Solution: 

(x + y) (2x + 5) - (x + y) (x + 3) 

= (x + y) [(2x + 5) - (x + 3)]

= (x + y) [2x + 5 - x -3]

= (x + y) (x + 2)


(ii) 6ab - b2 + 12ac - 2bc 

Solution: 

6ab - b2 + 12ac - 2bc

= b(6a - b) + 2c(6a - b) 

= (6a - b) (b + 2c)

`