Solve [7x^{2}:7x+9x^{2}yz:(3xyz)]^2:8+(4x)^2}:(9x^2)*(1/2x^2)

$$[ 7 x ^ { 2 } : 7 x + 9 x ^ { 2 } y z : ( 3 x y z ) ] ^ { 2 } : 8 + ( 4 x ) ^ { 2 } \} : ( 9 x ^ { 2 } ) \cdot ( \frac { 1 } { 2 } x ^ { 2 } )$$

Evaluate

$$\frac{x^{2}\left(x^{4}+6x^{2}+137\right)}{8}$$

Short Solution Steps

Cancel out 7 and 7.

$$\frac{\left(x^{2}x+\frac{9x^{2}yz}{3xyz}\right)^{2}}{8}+\left(4x\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\left(x^{3}+\frac{9x^{2}yz}{3xyz}\right)^{2}}{8}+\left(4x\right)^{2}$$

Cancel out 3xyz in both numerator and denominator.

$$\frac{\left(x^{3}+3x\right)^{2}}{8}+\left(4x\right)^{2}$$

Expand \left(4x\right)^{2}.

$$\frac{\left(x^{3}+3x\right)^{2}}{8}+4^{2}x^{2}$$

Calculate 4 to the power of 2 and get 16.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 16x^{2} times \frac{8}{8}.

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

Since \frac{\left(x^{3}+3x\right)^{2}}{8} and \frac{8\times 16x^{2}}{8} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x^{3}+3x\right)^{2}+8\times 16x^{2}.

$$\frac{x^{6}+6x^{4}+9x^{2}+128x^{2}}{8}$$

Combine like terms in x^{6}+6x^{4}+9x^{2}+128x^{2}.

$$\frac{x^{6}+6x^{4}+137x^{2}}{8}$$

Expand

$$\frac{x^{6}}{8}+\frac{3x^{4}}{4}+\frac{137x^{2}}{8}$$

Short Solution Steps

Cancel out 7 and 7.

$$\frac{\left(x^{2}x+\frac{9x^{2}yz}{3xyz}\right)^{2}}{8}+\left(4x\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\left(x^{3}+\frac{9x^{2}yz}{3xyz}\right)^{2}}{8}+\left(4x\right)^{2}$$

Cancel out 3xyz in both numerator and denominator.

$$\frac{\left(x^{3}+3x\right)^{2}}{8}+\left(4x\right)^{2}$$

Expand \left(4x\right)^{2}.

$$\frac{\left(x^{3}+3x\right)^{2}}{8}+4^{2}x^{2}$$

Calculate 4 to the power of 2 and get 16.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 16x^{2} times \frac{8}{8}.

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

Since \frac{\left(x^{3}+3x\right)^{2}}{8} and \frac{8\times 16x^{2}}{8} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x^{3}+3x\right)^{2}+8\times 16x^{2}.

$$\frac{x^{6}+6x^{4}+9x^{2}+128x^{2}}{8}$$

Combine like terms in x^{6}+6x^{4}+9x^{2}+128x^{2}.

$$\frac{x^{6}+6x^{4}+137x^{2}}{8}$$