Question

Factorise the following completely 6x(squared) + 11xy + 5y(squared)

Answer 1

Answer:

$\boxed{\sf (x + y)(6x + 5y)}$

Step-by-step explanation:

Factor the following:

$\sf \implies 6 {x}^{2} + 11xy + 5 {y}^{2}$

The coefficient of x² is 6 and the coefficient of y² is 5. The product of 6 and 5 is 30. The factors of 30 which sum to 11 are 5 and 6.

So,

$\sf \implies 6 {x}^{2} + (6 + 5)xy + 5 {y}^{2}$

$\sf \implies 6 {x}^{2} + 6xy + 5xy + 5 {y}^{2}$

$\sf \implies 6x(x + y) + 5y(x + y)$

Factor (x + y) from 6x(x + y) + 5y(x + y):

$\sf \implies (x + y)(6x + 5y)$