Question

a(a+c) -b(b+c) factorise using identies

Answer 1

Answer:

(a-c) [(a+b)-c]

Step-by-step explanation:

a²+ac-b²-bc

a²-b²+ac-bc

a²-b²=(a+b)(a-b)

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

(a-b)[(a+b)-c]

Answer 2

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

Given :

The expression a(a + c) - b(b + c)

To find :

Factorise the expression

Formula :

a² - b² = ( a + b ) ( a - b )

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

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

Step 2 of 2 :

Factorise the expression

We use the formula a² - b² = ( a + b ) ( a - b )

$\displaystyle \sf{ a(a + c) -b(b + c) }$

$\displaystyle \sf{ = {a}^{2} + ac - {b}^{2} - bc }$

$\displaystyle \sf{ = {a}^{2} - {b}^{2} + ac - bc }$

$\displaystyle \sf{ = (a + b)(a - b) + c(a - b) }$

$\displaystyle \sf{ = (a - b)(a + b + c) }$