What is factor 25x^2-(x+2y+4z)^2 ?

The solution to factor 25x^2-(x+2y+4z)^2 is 4(3x+y+2z)(2x-y-2z)

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factor 25x^2-(x+2y+4z)^2

factor

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

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

Solution steps

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

Simplify

25 x^{2} : (5 x)^{2}

= (5 x)^{2} - (x + 2 y + 4 z)^{2}

Apply Difference of Two Squares Formula:

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

(5 x)^{2} - (x + 2 y + 4 z)^{2} = (5 x + (x + 2 y + 4 z)) (5 x - (x + 2 y + 4 z))

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

Simplify

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

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

Factor

6 x + 2 y + 4 z : 2 (3 x + y + 2 z)

Factor

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

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

Multiply the numbers:

2 \cdot 2 = 4

= 4 (3 x + y + 2 z) (2 x - y - 2 z)

∣ x + 5 ∣ < 4

b^{4} - 7 b^{2} - 144

2 k^{2} + 2 = 4 k

- \frac{7}{2} \cdot \frac{1}{6}

(\frac{1}{2})^{2} + (\frac{1}{4})^{2}

What is factor 25x^2-(x+2y+4z)^2 ?
The solution to factor 25x^2-(x+2y+4z)^2 is 4(3x+y+2z)(2x-y-2z)