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

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

Evaluate

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

Solution Steps

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

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

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

$$8x^{3}+36x^{2}+54x+27-\left(x^{3}-12x^{2}+48x-64\right)$$

To find the opposite of x^{3}-12x^{2}+48x-64, find the opposite of each term.

$$8x^{3}+36x^{2}+54x+27-x^{3}+12x^{2}-48x+64$$

Combine 8x^{3} and -x^{3} to get 7x^{3}.

$$7x^{3}+36x^{2}+54x+27+12x^{2}-48x+64$$

Combine 36x^{2} and 12x^{2} to get 48x^{2}.

$$7x^{3}+48x^{2}+54x+27-48x+64$$

Combine 54x and -48x to get 6x.

$$7x^{3}+48x^{2}+6x+27+64$$

Add 27 and 64 to get 91.

$$7x^{3}+48x^{2}+6x+91$$

Expand

$$7x^{3}+48x^{2}+6x+91$$

Solution Steps

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

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

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

$$8x^{3}+36x^{2}+54x+27-\left(x^{3}-12x^{2}+48x-64\right)$$

To find the opposite of x^{3}-12x^{2}+48x-64, find the opposite of each term.

$$8x^{3}+36x^{2}+54x+27-x^{3}+12x^{2}-48x+64$$

Combine 8x^{3} and -x^{3} to get 7x^{3}.

$$7x^{3}+36x^{2}+54x+27+12x^{2}-48x+64$$

Combine 36x^{2} and 12x^{2} to get 48x^{2}.

$$7x^{3}+48x^{2}+54x+27-48x+64$$

Combine 54x and -48x to get 6x.

$$7x^{3}+48x^{2}+6x+27+64$$

Add 27 and 64 to get 91.

$$7x^{3}+48x^{2}+6x+91$$