Solve f(x)=3(x^2+7)(x^2+8)^2

$$f ( x ) = 3 ( x ^ { 2 } + 7 ) ( x ^ { 2 } + 8 ) ^ { 2 }$$

Evaluate

$$3\left(x^{2}+7\right)\left(x^{2}+8\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+8\right)^{2}.

$$3\left(x^{2}+7\right)\left(\left(x^{2}\right)^{2}+16x^{2}+64\right)$$

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

$$3\left(x^{2}+7\right)\left(x^{4}+16x^{2}+64\right)$$

Use the distributive property to multiply 3 by x^{2}+7.

$$\left(3x^{2}+21\right)\left(x^{4}+16x^{2}+64\right)$$

Use the distributive property to multiply 3x^{2}+21 by x^{4}+16x^{2}+64 and combine like terms.

$$3x^{6}+69x^{4}+528x^{2}+1344$$

Expand

$$3x^{6}+69x^{4}+528x^{2}+1344$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+8\right)^{2}.

$$3\left(x^{2}+7\right)\left(\left(x^{2}\right)^{2}+16x^{2}+64\right)$$

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

$$3\left(x^{2}+7\right)\left(x^{4}+16x^{2}+64\right)$$

Use the distributive property to multiply 3 by x^{2}+7.

$$\left(3x^{2}+21\right)\left(x^{4}+16x^{2}+64\right)$$

Use the distributive property to multiply 3x^{2}+21 by x^{4}+16x^{2}+64 and combine like terms.

$$3x^{6}+69x^{4}+528x^{2}+1344$$