What is factor 1-(2y-3)^2 ?

The solution to factor 1-(2y-3)^2 is 4(-1+y)(-y+2)

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factor 1-(2y-3)^2

factor

1 - (2 y - 3)^{2}

4 (- 1 + y) (- y + 2)

Solution steps

1 - (2 y - 3)^{2}

Rewrite

1

1^{2}

= 1^{2} - (2 y - 3)^{2}

Apply Difference of Two Squares Formula:

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

1^{2} - (2 y - 3)^{2} = (1 + (2 y - 3)) (1 - (2 y - 3))

= (1 + (2 y - 3)) (1 - (2 y - 3))

Simplify

(1 + (2 y - 3)) (1 - (2 y - 3)) : (- 2 + 2 y) (- 2 y + 4)

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

Factor

- 2 + 2 y : 2 (- 1 + y)

Factor

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

= 2 (- 1 + y) \cdot 2 (- y + 2)

Multiply the numbers:

2 \cdot 2 = 4

= 4 (- 1 + y) (- y + 2)

12 ab - 8 a

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

3 x^{2} - 12 x + 11 = x

lo g_{4} (32) + lo g_{4} (2)

5 x = 45