Solve left(3x^2-4right)^2-9x(x^3+3x)+(x-3)(2x+5)

$${ \left(3 { x }^{ 2 } -4 \right) }^{ 2 } -9x( { x }^{ 3 } +3x)+(x-3)(2x+5)$$

Evaluate

$$1-x-49x^{2}$$

Solution Steps

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

$$9\left(x^{2}\right)^{2}-24x^{2}+16-9x\left(x^{3}+3x\right)+\left(x-3\right)\left(2x+5\right)$$

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

$$9x^{4}-24x^{2}+16-9x\left(x^{3}+3x\right)+\left(x-3\right)\left(2x+5\right)$$

Use the distributive property to multiply x-3 by 2x+5 and combine like terms.

$$9x^{4}-24x^{2}+16-9x\left(x^{3}+3x\right)+2x^{2}-x-15$$

Use the distributive property to multiply -9x by x^{3}+3x.

$$9x^{4}-24x^{2}+16-9x^{4}-27x^{2}+2x^{2}-x-15$$

Combine 9x^{4} and -9x^{4} to get 0.

$$-24x^{2}+16-27x^{2}+2x^{2}-x-15$$

Combine -24x^{2} and -27x^{2} to get -51x^{2}.

$$-51x^{2}+16+2x^{2}-x-15$$

Combine -51x^{2} and 2x^{2} to get -49x^{2}.

$$-49x^{2}+16-x-15$$

Subtract 15 from 16 to get 1.

$$-49x^{2}+1-x$$

Expand

$$1-x-49x^{2}$$

Solution Steps

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

$$9\left(x^{2}\right)^{2}-24x^{2}+16-9x\left(x^{3}+3x\right)+\left(x-3\right)\left(2x+5\right)$$

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

$$9x^{4}-24x^{2}+16-9x\left(x^{3}+3x\right)+\left(x-3\right)\left(2x+5\right)$$

Use the distributive property to multiply x-3 by 2x+5 and combine like terms.

$$9x^{4}-24x^{2}+16-9x\left(x^{3}+3x\right)+2x^{2}-x-15$$

Use the distributive property to multiply -9x by x^{3}+3x.

$$9x^{4}-24x^{2}+16-9x^{4}-27x^{2}+2x^{2}-x-15$$

Combine 9x^{4} and -9x^{4} to get 0.

$$-24x^{2}+16-27x^{2}+2x^{2}-x-15$$

Combine -24x^{2} and -27x^{2} to get -51x^{2}.

$$-51x^{2}+16+2x^{2}-x-15$$

Combine -51x^{2} and 2x^{2} to get -49x^{2}.

$$-49x^{2}+16-x-15$$

Subtract 15 from 16 to get 1.

$$-49x^{2}+1-x$$