What is factor 125(x+2)^3+64(x-5)^3 ?

The solution to factor 125(x+2)^3+64(x-5)^3 is 7(9x-10)(3x^2+100)

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factor 125(x+2)^3+64(x-5)^3

factor

125 (x + 2)^{3} + 64 (x - 5)^{3}

7 (9 x - 10) (3 x^{2} + 100)

Solution steps

125 (x + 2)^{3} + 64 (x - 5)^{3}

Rewrite

125 (x + 2)^{3} + 64 (x - 5)^{3}

(5 (x + 2))^{3} + (4 (x - 5))^{3}

= (5 (x + 2))^{3} + (4 (x - 5))^{3}

Apply Sum of Cubes Formula:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(5 (x + 2))^{3} + (4 (x - 5))^{3} = (5 (x + 2) + 4 (x - 5)) (5^{2} (x + 2)^{2} - 5 \cdot 4 (x - 5) (x + 2) + 4^{2} (x - 5)^{2})

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

Refine

= (4 (x - 5) + 5 (x + 2)) (16 (x - 5)^{2} - 20 (x - 5) (x + 2) + 25 (x + 2)^{2})

Factor

25 (x + 2)^{2} - 20 (x - 5) (x + 2) + 16 (x - 5)^{2} : 7 (3 x^{2} + 100)

= 7 (4 (x - 5) + 5 (x + 2)) (3 x^{2} + 100)

Expand

4 (x - 5) + 5 (x + 2) : 9 x - 10

= 7 (9 x - 10) (3 x^{2} + 100)

(\frac{1}{4})^{x}

x (x - 4) = 5

25 c^{2} - 20 c + 4

\frac{X}{4} + \frac{X}{3} \leq 90

\frac{5}{2 5 - 6}

What is factor 125(x+2)^3+64(x-5)^3 ?
The solution to factor 125(x+2)^3+64(x-5)^3 is 7(9x-10)(3x^2+100)