Solve (3-16x)left(x+4right)^2

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

Expand

$$48-232x-125x^{2}-16x^{3}$$

Solution Steps

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

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

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

$$-125x^{2}-232x+48-16x^{3}$$

Evaluate

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

Solution Steps

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

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

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

$$-125x^{2}-232x+48-16x^{3}$$