What is factor (3x+y)^2-(3y-x)^2 ?

The solution to factor (3x+y)^2-(3y-x)^2 is 4(x+2y)(2x-y)

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factor (3x+y)^2-(3y-x)^2

factor

(3 x + y)^{2} - (3 y - x)^{2}

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

Solution steps

(3 x + y)^{2} - (3 y - x)^{2}

Apply Difference of Two Squares Formula:

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

(3 x + y)^{2} - (3 y - x)^{2} = ((3 x + y) + (3 y - x)) ((3 x + y) - (3 y - x))

= ((3 x + y) + (3 y - x)) ((3 x + y) - (3 y - x))

Simplify

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

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

Factor

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

Factor

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

= 2 (x + 2 y) \cdot 2 (2 x - y)

Multiply the numbers:

2 \cdot 2 = 4

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

- \frac{1}{2} \div \frac{2}{5}

x^{3} - 5 x^{2} + 2 x - 10

x^{2} - 2 x y + x - 2 y

b^{2} - 16 c^{2}

\frac{3}{5} \cdot 40

What is factor (3x+y)^2-(3y-x)^2 ?
The solution to factor (3x+y)^2-(3y-x)^2 is 4(x+2y)(2x-y)