What is (2x-3)^2+2(2x-3)-1 ?

The solution to (2x-3)^2+2(2x-3)-1 is 4x^2-8x+2

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simplify (2x-3)^2+2(2x-3)-1

simplify

(2 x - 3)^{2} + 2 (2 x - 3) - 1

4 x^{2} - 8 x + 2

Solution steps

(2 x - 3)^{2} + 2 (2 x - 3) - 1

Expand

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

= 4 x^{2} - 12 x + 9 + 2 (2 x - 3) - 1

Expand

2 (2 x - 3) : 4 x - 6

= 4 x^{2} - 12 x + 9 + 4 x - 6 - 1

Group like terms

= 4 x^{2} - 12 x + 4 x + 9 - 6 - 1

Add similar elements:

- 12 x + 4 x = - 8 x

= 4 x^{2} - 8 x + 9 - 6 - 1

Subtract the numbers:

9 - 6 - 1 = 2

= 4 x^{2} - 8 x + 2

2 cos^{2} (2 x) - 1

e^{l n (5) - l n (2)}

(4 x - 2)^{2}

3 (x 3 + 4)^{2} - 4

1 \frac{3}{8} - \frac{7}{8}