Question

Factorize
(a + 2b) 2 - (a + 2b)(3a - 7b) using algebraic identities

please provide a step by step explanation​

Answer 1

ANSWER:

$2 {a}^{2} + 5ab + 18 {b}^{2}$

EXPLANATION:

${(a + 2b)}^{2} - (a + 2b)(3a - 7b)$

$= ( \: {(a)}^{2} + 2(a)(2b) + {(2b)}^{2} \: ) - ( \: a(3a - 7b) + 2b(3a - 7b) \: )$

$= ( {a}^{2} + 4ab + 4 {b}^{2}) - (3 {a}^{2} - 7ab + 6ab - 14 {b}^{2} )$

$= ( {a}^{2} + 4ab + 4 {b}^{2}) - (3 {a}^{2} - ab - 14 {b}^{2} )$

$= {a}^{2} + 4ab + 4 {b}^{2} - 3 {a}^{2} + ab + 14 {b}^{2}$

$= {a}^{2} - 3{a}^{2} + 4ab + ab + 4 {b}^{2} + 14 {b}^{2}$

$= - 2 {a}^{2} + 5ab + 18 {b}^{2}$

I hope it helps you. Please mark me as BRAINLIEST if you like.