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

The solution to (3x+2)^2-2(x+2)(x-2)-(x-1)^2 is 6x^2+14x+11

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

simplify

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

6 x^{2} + 14 x + 11

Solution steps

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

Expand

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

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

Expand

- 2 (x + 2) (x - 2) : - 2 x^{2} + 8

= 9 x^{2} + 12 x + 4 - 2 x^{2} + 8 - (x - 1)^{2}

Expand

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

= 9 x^{2} + 12 x + 4 - 2 x^{2} + 8 - x^{2} + 2 x - 1

Group like terms

= 9 x^{2} - 2 x^{2} - x^{2} + 12 x + 2 x + 4 + 8 - 1

Add similar elements:

9 x^{2} - 2 x^{2} - x^{2} = 6 x^{2}

= 6 x^{2} + 12 x + 2 x + 4 + 8 - 1

Add similar elements:

12 x + 2 x = 14 x

= 6 x^{2} + 14 x + 4 + 8 - 1

Add the numbers:

4 + 8 - 1 = 11

= 6 x^{2} + 14 x + 11

2 π (3)

2 π (4)

3 (x - 1) + 4 (x + 2)

\frac{4}{5} \cdot 20

\frac{2}{3} \cdot (- 4)

What is (3x+2)^2-2(x+2)(x-2)-(x-1)^2 ?
The solution to (3x+2)^2-2(x+2)(x-2)-(x-1)^2 is 6x^2+14x+11