What is factor-(x+2y)^2+16(x+y)^2 ?

The solution to factor-(x+2y)^2+16(x+y)^2 is (5x+6y)(3x+2y)

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factor-(x+2y)^2+16(x+y)^2

factor

- (x + 2 y)^{2} + 16 (x + y)^{2}

(5 x + 6 y) (3 x + 2 y)

Solution steps

- (x + 2 y)^{2} + 16 (x + y)^{2}

Rewrite

16 (x + y)^{2} - (x + 2 y)^{2}

(4 (x + y))^{2} - (x + 2 y)^{2}

= (4 (x + y))^{2} - (x + 2 y)^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(4 (x + y))^{2} - (x + 2 y)^{2} = (4 (x + y) + (x + 2 y)) (4 (x + y) - (x + 2 y))

= (4 (x + y) + (x + 2 y)) (4 (x + y) - (x + 2 y))

Refine

= (x + 2 y + 4 (x + y)) (4 (x + y) - x - 2 y)

Expand

4 (x + y) + x + 2 y : 5 x + 6 y

= (5 x + 6 y) (4 (x + y) - x - 2 y)

Expand

4 (x + y) - x - 2 y : 3 x + 2 y

= (5 x + 6 y) (3 x + 2 y)

2 (v - 4) - 10 = - 2 (- 1 + 4 v)

1 + \frac{1}{16}

\frac{n ^{2}}{n ^{4}}

3 \cdot z^{2} + 20 \cdot z - 11 = 0

2 x^{2} + 36 = 0

What is factor-(x+2y)^2+16(x+y)^2 ?
The solution to factor-(x+2y)^2+16(x+y)^2 is (5x+6y)(3x+2y)