Solve 4x*(x+6)^2-3x^2

$$4 x \cdot ( x + 6 ) ^ { 2 } - 3 x ^ { 2 }$$

Evaluate

$$x\left(4x^{2}+45x+144\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$4x\left(x^{2}+12x+36\right)-3x^{2}$$

Use the distributive property to multiply 4x by x^{2}+12x+36.

$$4x^{3}+48x^{2}+144x-3x^{2}$$

Combine 48x^{2} and -3x^{2} to get 45x^{2}.

$$4x^{3}+45x^{2}+144x$$

Expand

$$4x^{3}+45x^{2}+144x$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$4x\left(x^{2}+12x+36\right)-3x^{2}$$

Use the distributive property to multiply 4x by x^{2}+12x+36.

$$4x^{3}+48x^{2}+144x-3x^{2}$$

Combine 48x^{2} and -3x^{2} to get 45x^{2}.

$$4x^{3}+45x^{2}+144x$$