What is factor 5x^3+10^2-20^2-40 ?

The solution to factor 5x^3+10^2-20^2-40 is 5(x^3-68)

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factor 5x^3+10^2-20^2-40

factor

5 x^{3} + 1 0^{2} - 2 0^{2} - 40

5 (x^{3} - 68)

Solution steps

5 x^{3} + 1 0^{2} - 2 0^{2} - 40

10 = 2 \cdot 5

= 5^{1} x^{3} + (2 \cdot 5)^{2} - 2 0^{2} - 2^{3} \cdot 5^{1}

20 = 2^{2} \cdot 5

= 5^{1} x^{3} + 2^{2} \cdot 5^{2} - (2^{2} \cdot 5)^{2} - 2^{3} \cdot 5^{1}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

= 5^{1} x^{3} + 2^{2} \cdot 5^{2} - 5^{2} (2^{2})^{2} - 2^{3} \cdot 5^{1}

Rewrite as

= 5 x^{3} + 5 \cdot 20 - 5 \cdot 5 \cdot 2^{2 \cdot 2} - 5 \cdot 8

Factor out common term

5

= 5 (x^{3} + 20 - 5 \cdot 2^{2 \cdot 2} - 8)

Refine

= 5 (x^{3} - 68)

15 x + 15 y - b x - b y

c e^{x} + d e^{- x}

x^{6} y^{3} + 27 z^{3}

4 x y + 2 x z - 6 y - 3 z

a^{x - 1} b - b^{n - 1} a

What is factor 5x^3+10^2-20^2-40 ?
The solution to factor 5x^3+10^2-20^2-40 is 5(x^3-68)