Solve (x+6)^2(x+4)^2

$$( x + 6 ) ^ { 2 } ( x + 4 ) ^ { 2 }$$

Evaluate

$$\left(\left(x+4\right)\left(x+6\right)\right)^{2}$$

Solution Steps

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

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

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

$$\left(x^{2}+12x+36\right)\left(x^{2}+8x+16\right)$$

Use the distributive property to multiply x^{2}+12x+36 by x^{2}+8x+16 and combine like terms.

$$x^{4}+20x^{3}+148x^{2}+480x+576$$

Expand

$$x^{4}+20x^{3}+148x^{2}+480x+576$$

Solution Steps

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

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

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

$$\left(x^{2}+12x+36\right)\left(x^{2}+8x+16\right)$$

Use the distributive property to multiply x^{2}+12x+36 by x^{2}+8x+16 and combine like terms.

$$x^{4}+20x^{3}+148x^{2}+480x+576$$