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

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

Evaluate

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

Solution Steps

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

$$3\left(x^{2}-8x+16\right)\left(x^{2}+3\right)$$

Use the distributive property to multiply 3 by x^{2}-8x+16.

$$\left(3x^{2}-24x+48\right)\left(x^{2}+3\right)$$

Use the distributive property to multiply 3x^{2}-24x+48 by x^{2}+3 and combine like terms.

$$3x^{4}+57x^{2}-24x^{3}-72x+144$$

Expand

$$3x^{4}-24x^{3}+57x^{2}-72x+144$$

Solution Steps

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

$$3\left(x^{2}-8x+16\right)\left(x^{2}+3\right)$$

Use the distributive property to multiply 3 by x^{2}-8x+16.

$$\left(3x^{2}-24x+48\right)\left(x^{2}+3\right)$$

Use the distributive property to multiply 3x^{2}-24x+48 by x^{2}+3 and combine like terms.

$$3x^{4}+57x^{2}-24x^{3}-72x+144$$