Q. 6.82

Factor completely: $16 x^{2} + 24 x y - 4 x - 6 y$

Verified

Answer

The required factors are $2 (4 x - 1) (2 x + 3 y)$

1Step 1. Given Information

The given expression is $16 x^{2} + 24 x y - 4 x - 6 y$

2Step 2. Calculation

We will factor the expression by taking the common factor outside the paranthesis.

$16 x^{2} + 24 x y - 4 x - 6 y = 2 [8 x^{2} + 12 x y - 2 x - 3 y] = 2 [4 x (2 x + 3 y) - 1 (2 x + 3 y)] = 2 (4 x - 1) (2 x + 3 y)$

3Step 3. Check

We will verify by multiplying the factors.

$2 (4 x - 1) (2 x + 3 y) = 2 [4 x (2 x + 3 y) - 1 (2 x + 3 y)] = 2 [8 x^{2} + 12 x y - 2 x - 3 y] = 16 x^{2} + 24 x y - 4 x - 6 y$