Question

Factorise the following: 5 ( 3x + y)2 + 6( 3x + y) - 8.​

Answer 1

Answer:

Step-by-step explanation:

Let (3x + y) = z. Then, the expression becomes:

5z2 + 6z - 8

= 5z2 + 10z - 4z - 8

= 5z(z + 2) - 4(z + 2)

= (z + 2)(5z - 4)

= (3x + y + 2) [5(3x + y) - 4]

= (3x + y + 2) (15x + 5y - 4)

Answer 2

$\sf \: 5 {(3x + y)}^{2} + 6(3x + y) - 8 \\ \\ \sf \:Let \: (3x+y) = a. \\ \sf \: 5 {a}^{2} + 6a - 8 \\ \sf \implies \: 5 {a}^{2} + 10a - 4a - 8 \\ \sf \implies \: 5a(a + 2) - 4(a + 2) \\ \sf \implies \: (a + 2)(5a - 4) \\ \\ \sf \: Put \: the \: value \: of \: a \: and \: substitute, \\ \sf \: (3x + y + 2) \: (5(3x + y) - 4) \\ \red{\sf \implies{(3x -y + 2) \: (15x + 5y - 4) \: \: \: ....(ans)}}$