What is (5x^2+13x-4)-(17x^2+7x-19)+(5x-7)(3x+1) ?

The solution to (5x^2+13x-4)-(17x^2+7x-19)+(5x-7)(3x+1) is 3x^2-10x+8

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simplify (5x^2+13x-4)-(17x^2+7x-19)+(5x-7)(3x+1)

simplify

(5 x^{2} + 13 x - 4) - (17 x^{2} + 7 x - 19) + (5 x - 7) (3 x + 1)

3 x^{2} - 10 x + 8

Solution steps

(5 x^{2} + 13 x - 4) - (17 x^{2} + 7 x - 19) + (5 x - 7) (3 x + 1)

Apply rule:

(a) = a

(5 x^{2} + 13 x - 4) = 5 x^{2} + 13 x - 4

= 5 x^{2} + 13 x - 4 - (17 x^{2} + 7 x - 19) + (5 x - 7) (3 x + 1)

Apply the distributive law:

- (a + b) = - a - b

- (17 x^{2} + 7 x - 19) = - 17 x^{2} - 7 x + 19

= 5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + (5 x - 7) (3 x + 1)

Expand

(5 x - 7) (3 x + 1) : 15 x^{2} - 16 x - 7

= 5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + 15 x^{2} - 16 x - 7

Group like terms

= 5 x^{2} - 17 x^{2} + 15 x^{2} + 13 x - 7 x - 16 x - 4 + 19 - 7

Add similar elements:

5 x^{2} - 17 x^{2} + 15 x^{2} = 3 x^{2}

= 3 x^{2} + 13 x - 7 x - 16 x - 4 + 19 - 7

Add similar elements:

13 x - 7 x - 16 x = - 10 x

= 3 x^{2} - 10 x - 4 + 19 - 7

Add the numbers:

- 4 + 19 - 7 = 8

= 3 x^{2} - 10 x + 8

(5 - 3 i) (2 + 4 i)

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

m (x + 2) + n (x + 2) + (x + 2)

2 - \frac{1}{2 - \frac{2}{2 + \frac{1}{x}}}

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

What is (5x^2+13x-4)-(17x^2+7x-19)+(5x-7)(3x+1) ?
The solution to (5x^2+13x-4)-(17x^2+7x-19)+(5x-7)(3x+1) is 3x^2-10x+8