Question

Factorise (2a+3b)²+8(2a+3b)+15



Pls tell the answer​

Answer 1

Step-by-step explanation:

let 2a + 3b = x

${x}^{2} + 8x + 15 = 0\\ {x}^{2} + 5x + 3x + 15 = 0 \\ x(x + 5) + 3(x + 5) = 0 \\ (x + 5)(x + 3) = 0 \\ substitute \: x = 2a + 3b \\ (2a + 3b + 5)(2a + 3b + 3)$

verification

$(2a + 3b + 5)(2a + 3b + 3) \\ 4 {a}^{2} + 6ab + 6a + 6ab + 9 {b}^{2} + 9b + 10a + 15b + 15 \\ 4 {a}^{2} + 12ab + 9 {b}^{2} + 16a + 24b + 15 \\ {(2a)}^{2} + 12ab + {(3b)}^{2} + 8(2a + 3b) + 15 \\ {(2a + 3b)}^{2} + 8(2a + 3b) + 15$

hope you get your answer