What is factor (4y^2-12xy+9x^2)-4z^2 ?

The solution to factor (4y^2-12xy+9x^2)-4z^2 is (2y-3x+2z)(2y-3x-2z)

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factor (4y^2-12xy+9x^2)-4z^2

factor

(4 y^{2} - 12 x y + 9 x^{2}) - 4 z^{2}

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

Solution steps

(4 y^{2} - 12 x y + 9 x^{2}) - 4 z^{2}

Factor

4 y^{2} - 12 y x + 9 x^{2} : (2 y - 3 x)^{2}

= (2 y - 3 x)^{2} - 4 z^{2}

Simplify

4 z^{2} : (2 z)^{2}

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

Apply Difference of Two Squares Formula:

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

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

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

Apply rule:

(a) = a

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

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

81 x^{4} - 16 y^{2}

x \cdot x \cdot x \cdot x \cdot x^{2020}

3 w - \frac{7}{5} \frac{w ^{3}}{21} - 9 \frac{w}{27} w

(a + 3 + a - 3)^{2}

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

What is factor (4y^2-12xy+9x^2)-4z^2 ?
The solution to factor (4y^2-12xy+9x^2)-4z^2 is (2y-3x+2z)(2y-3x-2z)