Question

factorize (2a+b)^2-6a-3b-4

Answer 1

(2a + b)² - 6a - 3b - 4
(2a + b)² - 3(2a + b) - 4
y² - 3y - 4  [ put y = 2a + b ]
y² - 4y + y - 4 
y(y-4) + 1(y-4)
(y+1)(y-4)
(2a + b + 1)(2a + b - 4)

Answer 2

Answer:

The factorisation of $(2a + b)^2 - 6a - 3b- 4$ gives $(2a + b + 1)(2a + b - 4)=0$

To find:

Factorise the given expression $(2a + b)^2 - 6a - 3b-4$

Solution:

Given that

$\begin{array} { c } { ( 2 a + b ) ^ { 2 } - 6 a - 3 b - 4 } \\\\ { ( 2 a + b ) ^ { 2 } - 3 ( 2 a + b ) - 4 = 0 } \end{array}$

Assume $x=2a+b$

$\begin{array} { c } { x ^ { 2 } - 3 x - 4 = 0 } \\\\ { x ^ { 2 } - 4 x + x - 4 = 0 } \\\\ { x ( x - 4 ) + 1 ( x - 4 ) = 0 } \\\\ { ( x + 1 ) ( x - 4 ) = 0 } \end{array}$

Substitute $x=2a+b$ in the above equation, we will get

$(2a + b + 1)(2a + b - 4)=0$