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

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

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

simplify

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

- x^{2} + x - 4

Solution steps

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

Apply rule:

(a) = a

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

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

Apply the distributive law:

- (a - b) = - a + b

- (5 x^{2} - 1) = - 5 x^{2} + 1

= 4 x^{2} + x - 5 - 5 x^{2} + 1

Group like terms

= 4 x^{2} - 5 x^{2} + x - 5 + 1

Add similar elements:

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

= - x^{2} + x - 5 + 1

Add the numbers:

- 5 + 1 = - 4

= - x^{2} + x - 4

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

- 6 (- 8 - 22)

(x^{2} - y + z) (x^{2} + y - z)

5 x^{4} (x^{2})

53 - 3