Solve f(x)=(24x^{4}+28x^{4}+12x^2+14x^2)(8x)^2+2x^2)

$$f ( x ) = ( 24 x ^ { 4 } + 28 x ^ { 4 } + 12 x ^ { 2 } + 14 x ^ { 2 } ) ( 8 x ) ^ { 2 } + 2 x ^ { 2 } )$$

Evaluate

$$3328x^{6}+1664x^{4}+2x^{2}$$

Solution Steps

Combine 24x^{4} and 28x^{4} to get 52x^{4}.

$$\left(52x^{4}+12x^{2}+14x^{2}\right)\times \left(8x\right)^{2}+2x^{2}$$

Combine 12x^{2} and 14x^{2} to get 26x^{2}.

$$\left(52x^{4}+26x^{2}\right)\times \left(8x\right)^{2}+2x^{2}$$

Expand \left(8x\right)^{2}.

$$\left(52x^{4}+26x^{2}\right)\times 8^{2}x^{2}+2x^{2}$$

Calculate 8 to the power of 2 and get 64.

$$\left(52x^{4}+26x^{2}\right)\times 64x^{2}+2x^{2}$$

Use the distributive property to multiply 52x^{4}+26x^{2} by 64.

$$\left(3328x^{4}+1664x^{2}\right)x^{2}+2x^{2}$$

Use the distributive property to multiply 3328x^{4}+1664x^{2} by x^{2}.

$$3328x^{6}+1664x^{4}+2x^{2}$$

Expand

$$3328x^{6}+1664x^{4}+2x^{2}$$

Solution Steps

Combine 24x^{4} and 28x^{4} to get 52x^{4}.

$$\left(52x^{4}+12x^{2}+14x^{2}\right)\times \left(8x\right)^{2}+2x^{2}$$

Combine 12x^{2} and 14x^{2} to get 26x^{2}.

$$\left(52x^{4}+26x^{2}\right)\times \left(8x\right)^{2}+2x^{2}$$

Expand \left(8x\right)^{2}.

$$\left(52x^{4}+26x^{2}\right)\times 8^{2}x^{2}+2x^{2}$$

Calculate 8 to the power of 2 and get 64.

$$\left(52x^{4}+26x^{2}\right)\times 64x^{2}+2x^{2}$$

Use the distributive property to multiply 52x^{4}+26x^{2} by 64.

$$\left(3328x^{4}+1664x^{2}\right)x^{2}+2x^{2}$$

Use the distributive property to multiply 3328x^{4}+1664x^{2} by x^{2}.

$$3328x^{6}+1664x^{4}+2x^{2}$$