Solve (3x^2-2)^3*(-2x+3)=

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(3x^{2}-2\right)^{3}.

$$\left(27\left(x^{2}\right)^{3}-54\left(x^{2}\right)^{2}+36x^{2}-8\right)\left(-2x+3\right)$$

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

$$\left(27x^{6}-54\left(x^{2}\right)^{2}+36x^{2}-8\right)\left(-2x+3\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(27x^{6}-54x^{4}+36x^{2}-8\right)\left(-2x+3\right)$$

Use the distributive property to multiply 27x^{6}-54x^{4}+36x^{2}-8 by -2x+3.

$$-54x^{7}+81x^{6}+108x^{5}-162x^{4}-72x^{3}+108x^{2}+16x-24$$

Expand

$$-54x^{7}+81x^{6}+108x^{5}-162x^{4}-72x^{3}+108x^{2}+16x-24$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(3x^{2}-2\right)^{3}.

$$\left(27\left(x^{2}\right)^{3}-54\left(x^{2}\right)^{2}+36x^{2}-8\right)\left(-2x+3\right)$$

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

$$\left(27x^{6}-54\left(x^{2}\right)^{2}+36x^{2}-8\right)\left(-2x+3\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(27x^{6}-54x^{4}+36x^{2}-8\right)\left(-2x+3\right)$$

Use the distributive property to multiply 27x^{6}-54x^{4}+36x^{2}-8 by -2x+3.

$$-54x^{7}+81x^{6}+108x^{5}-162x^{4}-72x^{3}+108x^{2}+16x-24$$