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

The solution to (-x-4)^2-(-x-4)-1 is x^2+9x+19

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

simplify

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

x^{2} + 9 x + 19

Solution steps

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

Apply the distributive law:

- (- a - b) = a + b

- (- x - 4) = x + 4

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

Expand

(- x - 4)^{2} : x^{2} + 8 x + 16

= x^{2} + 8 x + 16 + x + 4 - 1

Group like terms

= x^{2} + 8 x + x + 16 + 4 - 1

Add similar elements:

8 x + x = 9 x

= x^{2} + 9 x + 16 + 4 - 1

Add the numbers:

16 + 4 - 1 = 19

= x^{2} + 9 x + 19

25 (x - y)^{2} - 4 (x + y)^{2}

4 r^{2} + 20 r + 25

2 + \frac{3}{8}

\frac{a x - a y}{3 a}