What is (4x-3)^2-(5x+3)^2 ?

The solution to (4x-3)^2-(5x+3)^2 is -9x^2-54x

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simplify (4x-3)^2-(5x+3)^2

simplify

(4 x - 3)^{2} - (5 x + 3)^{2}

- 9 x^{2} - 54 x

Solution steps

(4 x - 3)^{2} - (5 x + 3)^{2}

Expand

(4 x - 3)^{2} : 16 x^{2} - 24 x + 9

= 16 x^{2} - 24 x + 9 - (5 x + 3)^{2}

Expand

- (5 x + 3)^{2} : - 25 x^{2} - 30 x - 9

= 16 x^{2} - 24 x + 9 - 25 x^{2} - 30 x - 9

Group like terms

= 16 x^{2} - 25 x^{2} - 24 x - 30 x + 9 - 9

Add similar elements:

16 x^{2} - 25 x^{2} = - 9 x^{2}

= - 9 x^{2} - 24 x - 30 x + 9 - 9

Add similar elements:

- 24 x - 30 x = - 54 x

= - 9 x^{2} - 54 x + 9 - 9

Subtract the numbers:

9 - 9 = 0

= - 9 x^{2} - 54 x

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