Question

Factorise 25a^2 − 4b^2 + 28bc − 49c^2

Answer 1

Answer:

$\sf{}(5a + 2b - 7c) (5a - 2b + 7c)$

Step-by-step explanation:

$\sf{}25a^2 - 4b^2 + 28bc - 49c^2$

$\Rightarrow 25a^2 - (4b^2 - 28bc + 49c^2]$

$\sf{}\Rightarrow (5a)^2 - [(2b)^2 - 2 \times 2b \times 7c + (7c)^2]$

$\sf{} \Rightarrow (5a)^2 - [(2b - 7c)^2]$

$\sf{}[Using\ identity\ (a - b)^2 = a^2 - 2ab + b^2]$

$\sf{} \Rightarrow [5a + (2b - 7c)] [5a - (2b - 7c)]$

$\sf{} [Using\ identity\ (a^2 - b^2)= (a - b) (a + b)]$

$\sf{} \Rightarrow (5a + 2b - 7c) (5a - 2b + 7c)$

Answer 2

Refer the image below. Hope it helps!