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

The solution to (3x+2)^2-(2x-3)^2 is 5x^2+24x-5

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

simplify

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

5 x^{2} + 24 x - 5

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

9 x^{2} - 4 x^{2} = 5 x^{2}

= 5 x^{2} + 12 x + 12 x + 4 - 9

Add similar elements:

12 x + 12 x = 24 x

= 5 x^{2} + 24 x + 4 - 9

Subtract the numbers:

4 - 9 = - 5

= 5 x^{2} + 24 x - 5

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

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

e^{\frac{- x ^{2}}{4}}

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

c^{4} + 3 c^{2} \cdot d^{2} - 4 d^{4}