What is factor 4(x+2y+z)^2-9(x-2y+z)^2 ?

The solution to factor 4(x+2y+z)^2-9(x-2y+z)^2 is (5x-2y+5z)(-x+10y-z)

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factor 4(x+2y+z)^2-9(x-2y+z)^2

factor

4 (x + 2 y + z)^{2} - 9 (x - 2 y + z)^{2}

(5 x - 2 y + 5 z) (- x + 10 y - z)

Solution steps

4 (x + 2 y + z)^{2} - 9 (x - 2 y + z)^{2}

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

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

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

Apply Difference of Two Squares Formula:

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

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

= (2 (x + 2 y + z) + 3 (x - 2 y + z)) (2 (x + 2 y + z) - 3 (x - 2 y + z))

Simplify

(2 (x + 2 y + z) + 3 (x - 2 y + z)) (2 (x + 2 y + z) - 3 (x - 2 y + z)) : (5 x - 2 y + 5 z) (- x + 10 y - z)

= (5 x - 2 y + 5 z) (- x + 10 y - z)

\frac{2 ^{9}}{2 ^{5}}

a^{- 8}

lo g_{8.5} (320)

- 6 x > - 18

x^{2} - 6 x = 5

What is factor 4(x+2y+z)^2-9(x-2y+z)^2 ?
The solution to factor 4(x+2y+z)^2-9(x-2y+z)^2 is (5x-2y+5z)(-x+10y-z)