Solve (4x+2)^3(2x-1)^3

$$( 4 x + 2 ) ^ { 3 } ( 2 x - 1 ) ^ { 3 }$$

Evaluate

$$8\left(4x^{2}-1\right)^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(4x+2\right)^{3}.

$$\left(64x^{3}+96x^{2}+48x+8\right)\left(2x-1\right)^{3}$$

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2x-1\right)^{3}.

$$\left(64x^{3}+96x^{2}+48x+8\right)\left(8x^{3}-12x^{2}+6x-1\right)$$

Use the distributive property to multiply 64x^{3}+96x^{2}+48x+8 by 8x^{3}-12x^{2}+6x-1 and combine like terms.

$$512x^{6}-384x^{4}+96x^{2}-8$$

Expand

$$512x^{6}-384x^{4}+96x^{2}-8$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(4x+2\right)^{3}.

$$\left(64x^{3}+96x^{2}+48x+8\right)\left(2x-1\right)^{3}$$

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2x-1\right)^{3}.

$$\left(64x^{3}+96x^{2}+48x+8\right)\left(8x^{3}-12x^{2}+6x-1\right)$$

Use the distributive property to multiply 64x^{3}+96x^{2}+48x+8 by 8x^{3}-12x^{2}+6x-1 and combine like terms.

$$512x^{6}-384x^{4}+96x^{2}-8$$