What is (x+3)(x+5)-(x+10)(x-2) ?

The solution to (x+3)(x+5)-(x+10)(x-2) is 35

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simplify (x+3)(x+5)-(x+10)(x-2)

simplify

(x + 3) (x + 5) - (x + 10) (x - 2)

35

Solution steps

(x + 3) (x + 5) - (x + 10) (x - 2)

Expand

(x + 3) (x + 5) : x^{2} + 8 x + 15

= x^{2} + 8 x + 15 - (x + 10) (x - 2)

Expand

- (x + 10) (x - 2) : - x^{2} - 8 x + 20

= x^{2} + 8 x + 15 - x^{2} - 8 x + 20

Group like terms

= x^{2} - x^{2} + 8 x - 8 x + 15 + 20

Add similar elements:

x^{2} - x^{2} = 0

= 8 x - 8 x + 15 + 20

Add similar elements:

8 x - 8 x = 0

= 15 + 20

Add the numbers:

15 + 20 = 35

= 35

\frac{cos ^{2} ( x )}{sin ^{2} ( x )}

(x + 10) (x^{2} - 10 x + 100) - (x + 5) (x^{2} - 5 x + 25)

- sin^{2} (x) + cos^{2} (x)

\frac{1}{csc ( x )}