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

The solution to (x-4)^3+3x(x-4)^2 is 4x^3-36x^2+96x-64

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

simplify

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

4 x^{3} - 36 x^{2} + 96 x - 64

Solution steps

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

Expand

(x - 4)^{3} : x^{3} - 12 x^{2} + 48 x - 64

= x^{3} - 12 x^{2} + 48 x - 64 + 3 x (x - 4)^{2}

Expand

3 x (x - 4)^{2} : 3 x^{3} - 24 x^{2} + 48 x

= x^{3} - 12 x^{2} + 48 x - 64 + 3 x^{3} - 24 x^{2} + 48 x

Group like terms

= x^{3} + 3 x^{3} - 12 x^{2} - 24 x^{2} + 48 x + 48 x - 64

Add similar elements:

x^{3} + 3 x^{3} = 4 x^{3}

= 4 x^{3} - 12 x^{2} - 24 x^{2} + 48 x + 48 x - 64

Add similar elements:

- 12 x^{2} - 24 x^{2} = - 36 x^{2}

= 4 x^{3} - 36 x^{2} + 48 x + 48 x - 64

Add similar elements:

48 x + 48 x = 96 x

= 4 x^{3} - 36 x^{2} + 96 x - 64

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

(\frac{7}{4} x - 5) + (2 y - 3.5) + (- \frac{1}{4} x + 5)

\frac{x}{x ^{5}}

(3 + x)^{3}

\frac{x ^{2} - 8 x + 16}{3 x - 12}

What is (x-4)^3+3x(x-4)^2 ?
The solution to (x-4)^3+3x(x-4)^2 is 4x^3-36x^2+96x-64