Solve 8left(2x-1right)^3+27left(x+2right)^3

$$8 { \left(2x-1 \right) }^{ 3 } +27 { \left(x+2 \right) }^{ 3 }$$

Evaluate

$$\left(7x+4\right)\left(13x^{2}+2x+52\right)$$

Solution Steps

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

$$8\left(8x^{3}-12x^{2}+6x-1\right)+27\left(x+2\right)^{3}$$

Use the distributive property to multiply 8 by 8x^{3}-12x^{2}+6x-1.

$$64x^{3}-96x^{2}+48x-8+27\left(x+2\right)^{3}$$

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

$$64x^{3}-96x^{2}+48x-8+27\left(x^{3}+6x^{2}+12x+8\right)$$

Use the distributive property to multiply 27 by x^{3}+6x^{2}+12x+8.

$$64x^{3}-96x^{2}+48x-8+27x^{3}+162x^{2}+324x+216$$

Combine 64x^{3} and 27x^{3} to get 91x^{3}.

$$91x^{3}-96x^{2}+48x-8+162x^{2}+324x+216$$

Combine -96x^{2} and 162x^{2} to get 66x^{2}.

$$91x^{3}+66x^{2}+48x-8+324x+216$$

Combine 48x and 324x to get 372x.

$$91x^{3}+66x^{2}+372x-8+216$$

Add -8 and 216 to get 208.

$$91x^{3}+66x^{2}+372x+208$$

Expand

$$91x^{3}+66x^{2}+372x+208$$

Solution Steps

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

$$8\left(8x^{3}-12x^{2}+6x-1\right)+27\left(x+2\right)^{3}$$

Use the distributive property to multiply 8 by 8x^{3}-12x^{2}+6x-1.

$$64x^{3}-96x^{2}+48x-8+27\left(x+2\right)^{3}$$

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

$$64x^{3}-96x^{2}+48x-8+27\left(x^{3}+6x^{2}+12x+8\right)$$

Use the distributive property to multiply 27 by x^{3}+6x^{2}+12x+8.

$$64x^{3}-96x^{2}+48x-8+27x^{3}+162x^{2}+324x+216$$

Combine 64x^{3} and 27x^{3} to get 91x^{3}.

$$91x^{3}-96x^{2}+48x-8+162x^{2}+324x+216$$

Combine -96x^{2} and 162x^{2} to get 66x^{2}.

$$91x^{3}+66x^{2}+48x-8+324x+216$$

Combine 48x and 324x to get 372x.

$$91x^{3}+66x^{2}+372x-8+216$$

Add -8 and 216 to get 208.

$$91x^{3}+66x^{2}+372x+208$$