What is (x+1)(x+2)-(x+3)^2+(x-3)^2-(x-4)(x-5) ?

The solution to (x+1)(x+2)-(x+3)^2+(x-3)^2-(x-4)(x-5) is -18

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simplify (x+1)(x+2)-(x+3)^2+(x-3)^2-(x-4)(x-5)

simplify

(x + 1) (x + 2) - (x + 3)^{2} + (x - 3)^{2} - (x - 4) (x - 5)

- 18

Solution steps

(x + 1) (x + 2) - (x + 3)^{2} + (x - 3)^{2} - (x - 4) (x - 5)

Expand

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

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

Expand

- (x + 3)^{2} : - x^{2} - 6 x - 9

= x^{2} + 3 x + 2 - x^{2} - 6 x - 9 + (x - 3)^{2} - (x - 4) (x - 5)

Expand

(x - 3)^{2} : x^{2} - 6 x + 9

= x^{2} + 3 x + 2 - x^{2} - 6 x - 9 + x^{2} - 6 x + 9 - (x - 4) (x - 5)

Expand

- (x - 4) (x - 5) : - x^{2} + 9 x - 20

= x^{2} + 3 x + 2 - x^{2} - 6 x - 9 + x^{2} - 6 x + 9 - x^{2} + 9 x - 20

Group like terms

= x^{2} - x^{2} + x^{2} - x^{2} + 3 x - 6 x - 6 x + 9 x + 2 - 9 + 9 - 20

Add similar elements:

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

= 3 x - 6 x - 6 x + 9 x + 2 - 9 + 9 - 20

Add similar elements:

3 x - 6 x - 6 x + 9 x = 0

= 2 - 9 + 9 - 20

Add the numbers:

2 - 9 + 9 - 20 = - 18

= - 18

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

\frac{4}{5 - 2}

sin (θ) + cot (θ) cos (θ)

f (x) x^{3}

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

What is (x+1)(x+2)-(x+3)^2+(x-3)^2-(x-4)(x-5) ?
The solution to (x+1)(x+2)-(x+3)^2+(x-3)^2-(x-4)(x-5) is -18