Solve (-3a^{2}x)^3*(-ax)^2-(-ax)^5(3a)^3

$$( - 3 a ^ { 2 } x ) ^ { 3 } \cdot ( - a x ) ^ { 2 } - ( - a x ) ^ { 5 } ( 3 a ) ^ { 3 }$$

Evaluate

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Solution Steps

Expand \left(-3a^{2}x\right)^{3}.

$$\left(-3\right)^{3}\left(a^{2}\right)^{3}x^{3}\left(\left(-a\right)x\right)^{2}-\left(\left(-a\right)x\right)^{5}\times \left(3a\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(-3\right)^{3}a^{6}x^{3}\left(\left(-a\right)x\right)^{2}-\left(\left(-a\right)x\right)^{5}\times \left(3a\right)^{3}$$

Calculate -3 to the power of 3 and get -27.

$$-27a^{6}x^{3}\left(\left(-a\right)x\right)^{2}-\left(\left(-a\right)x\right)^{5}\times \left(3a\right)^{3}$$

Expand \left(\left(-a\right)x\right)^{2}.

$$-27a^{6}x^{3}\left(-a\right)^{2}x^{2}-\left(\left(-a\right)x\right)^{5}\times \left(3a\right)^{3}$$

Calculate -a to the power of 2 and get a^{2}.

$$-27a^{6}x^{3}a^{2}x^{2}-\left(\left(-a\right)x\right)^{5}\times \left(3a\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$-27a^{8}x^{3}x^{2}-\left(\left(-a\right)x\right)^{5}\times \left(3a\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-27a^{8}x^{5}-\left(\left(-a\right)x\right)^{5}\times \left(3a\right)^{3}$$

Expand \left(\left(-a\right)x\right)^{5}.

$$-27a^{8}x^{5}-\left(-a\right)^{5}x^{5}\times \left(3a\right)^{3}$$

Expand \left(3a\right)^{3}.

$$-27a^{8}x^{5}-\left(-a\right)^{5}x^{5}\times 3^{3}a^{3}$$

Calculate 3 to the power of 3 and get 27.

$$-27a^{8}x^{5}-\left(-a\right)^{5}x^{5}\times 27a^{3}$$

Expand \left(-a\right)^{5}.

$$-27a^{8}x^{5}-\left(-1\right)^{5}a^{5}x^{5}\times 27a^{3}$$

Calculate -1 to the power of 5 and get -1.

$$-27a^{8}x^{5}-\left(-a^{5}x^{5}\times 27a^{3}\right)$$

Multiply -1 and -1 to get 1.

$$-27a^{8}x^{5}+a^{5}x^{5}\times 27a^{3}$$

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$-27a^{8}x^{5}+a^{8}x^{5}\times 27$$

Combine -27a^{8}x^{5} and a^{8}x^{5}\times 27 to get 0.

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Factor

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Solution Steps

Factor out common term \left(ax\right)^{2} by using distributive property.

$$\left(ax\right)^{2}\left(-27x^{3}a^{6}+27x^{3}a^{6}\right)$$

Consider -27x^{3}a^{6}+27x^{3}a^{6}. Simplify.

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