What is (4x^2+8x+15)+(x^2-x-27)-(x+5)(x-7) ?

The solution to (4x^2+8x+15)+(x^2-x-27)-(x+5)(x-7) is 4x^2+9x+23

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simplify (4x^2+8x+15)+(x^2-x-27)-(x+5)(x-7)

simplify

(4 x^{2} + 8 x + 15) + (x^{2} - x - 27) - (x + 5) (x - 7)

4 x^{2} + 9 x + 23

Solution steps

(4 x^{2} + 8 x + 15) + (x^{2} - x - 27) - (x + 5) (x - 7)

Simplify

(4 x^{2} + 8 x + 15) + (x^{2} - x - 27) - (x + 5) (x - 7) : 4 x^{2} + 8 x + 15 + x^{2} - x - 27 - (x + 5) (x - 7)

= 4 x^{2} + 8 x + 15 + x^{2} - x - 27 - (x + 5) (x - 7)

Group like terms

= 4 x^{2} + x^{2} + 8 x - x - (x + 5) (x - 7) + 15 - 27

Add similar elements:

4 x^{2} + x^{2} = 5 x^{2}

= 5 x^{2} + 8 x - x - (x + 5) (x - 7) + 15 - 27

Add similar elements:

8 x - x = 7 x

= 5 x^{2} + 7 x - (x + 5) (x - 7) + 15 - 27

Subtract the numbers:

15 - 27 = - 12

= 5 x^{2} + 7 x - (x + 5) (x - 7) - 12

Expand

- (x + 5) (x - 7) : - x^{2} + 2 x + 35

= 5 x^{2} + 7 x - x^{2} + 2 x + 35 - 12

Group like terms

= 5 x^{2} - x^{2} + 7 x + 2 x + 35 - 12

Add similar elements:

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

= 4 x^{2} + 7 x + 2 x + 35 - 12

Add similar elements:

7 x + 2 x = 9 x

= 4 x^{2} + 9 x + 35 - 12

Subtract the numbers:

35 - 12 = 23

= 4 x^{2} + 9 x + 23

59

\frac{cos ^{2} ( θ )}{sin ^{2} ( θ )} + csc (θ) sin (θ)

x^{3} (x + 2)

\frac{9}{7} \cdot (- \frac{9}{5})

\frac{\frac{6 x - 12}{x + 3}}{\frac{x - 2}{2 x + 6}}

What is (4x^2+8x+15)+(x^2-x-27)-(x+5)(x-7) ?
The solution to (4x^2+8x+15)+(x^2-x-27)-(x+5)(x-7) is 4x^2+9x+23