Solve (2x-3)^3+2x^2(x+6)-3(x+6)(7-5x)

$$( 2 x - 3 ) ^ { 3 } + 2 x ^ { 2 } ( x + 6 ) - 3 ( x + 6 ) ( 7 - 5 x )$$

Evaluate

$$10x^{3}-9x^{2}+123x-153$$

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}.

$$8x^{3}-36x^{2}+54x-27+2x^{2}\left(x+6\right)-3\left(x+6\right)\left(7-5x\right)$$

Use the distributive property to multiply 2x^{2} by x+6.

$$8x^{3}-36x^{2}+54x-27+2x^{3}+12x^{2}-3\left(x+6\right)\left(7-5x\right)$$

Combine 8x^{3} and 2x^{3} to get 10x^{3}.

$$10x^{3}-36x^{2}+54x-27+12x^{2}-3\left(x+6\right)\left(7-5x\right)$$

Combine -36x^{2} and 12x^{2} to get -24x^{2}.

$$10x^{3}-24x^{2}+54x-27-3\left(x+6\right)\left(7-5x\right)$$

Use the distributive property to multiply -3 by x+6.

$$10x^{3}-24x^{2}+54x-27+\left(-3x-18\right)\left(7-5x\right)$$

Use the distributive property to multiply -3x-18 by 7-5x and combine like terms.

$$10x^{3}-24x^{2}+54x-27+69x+15x^{2}-126$$

Combine 54x and 69x to get 123x.

$$10x^{3}-24x^{2}+123x-27+15x^{2}-126$$

Combine -24x^{2} and 15x^{2} to get -9x^{2}.

$$10x^{3}-9x^{2}+123x-27-126$$

Subtract 126 from -27 to get -153.

$$10x^{3}-9x^{2}+123x-153$$

Expand

$$10x^{3}-9x^{2}+123x-153$$

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}.

$$8x^{3}-36x^{2}+54x-27+2x^{2}\left(x+6\right)-3\left(x+6\right)\left(7-5x\right)$$

Use the distributive property to multiply 2x^{2} by x+6.

$$8x^{3}-36x^{2}+54x-27+2x^{3}+12x^{2}-3\left(x+6\right)\left(7-5x\right)$$

Combine 8x^{3} and 2x^{3} to get 10x^{3}.

$$10x^{3}-36x^{2}+54x-27+12x^{2}-3\left(x+6\right)\left(7-5x\right)$$

Combine -36x^{2} and 12x^{2} to get -24x^{2}.

$$10x^{3}-24x^{2}+54x-27-3\left(x+6\right)\left(7-5x\right)$$

Use the distributive property to multiply -3 by x+6.

$$10x^{3}-24x^{2}+54x-27+\left(-3x-18\right)\left(7-5x\right)$$

Use the distributive property to multiply -3x-18 by 7-5x and combine like terms.

$$10x^{3}-24x^{2}+54x-27+69x+15x^{2}-126$$

Combine 54x and 69x to get 123x.

$$10x^{3}-24x^{2}+123x-27+15x^{2}-126$$

Combine -24x^{2} and 15x^{2} to get -9x^{2}.

$$10x^{3}-9x^{2}+123x-27-126$$

Subtract 126 from -27 to get -153.

$$10x^{3}-9x^{2}+123x-153$$