Solve 2(x+5.2)(x^2-4)-x[(x+5.2)^2+x^2-100]

$$2 ( x + 5.2 ) ( x ^ { 2 } - 4 ) - x [ ( x + 5.2 ) ^ { 2 } + x ^ { 2 } - 100 ]$$

Evaluate

$$\frac{1624x}{25}-41.6$$

Solution Steps

Use the distributive property to multiply 2 by x+5.2.

$$\left(2x+10.4\right)\left(x^{2}-4\right)-x\left(\left(x+5.2\right)^{2}+x^{2}-100\right)$$

Use the distributive property to multiply 2x+10.4 by x^{2}-4.

$$2x^{3}-8x+10.4x^{2}-41.6-x\left(\left(x+5.2\right)^{2}+x^{2}-100\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5.2\right)^{2}.

$$2x^{3}-8x+10.4x^{2}-41.6-x\left(x^{2}+10.4x+27.04+x^{2}-100\right)$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{3}-8x+10.4x^{2}-41.6-x\left(2x^{2}+10.4x+27.04-100\right)$$

Subtract 100 from 27.04 to get -72.96.

$$2x^{3}-8x+10.4x^{2}-41.6-x\left(2x^{2}+10.4x-72.96\right)$$

Use the distributive property to multiply x by 2x^{2}+10.4x-72.96.

$$2x^{3}-8x+10.4x^{2}-41.6-\left(2x^{3}+10.4x^{2}-72.96x\right)$$

To find the opposite of 2x^{3}+10.4x^{2}-72.96x, find the opposite of each term.

$$2x^{3}-8x+10.4x^{2}-41.6-2x^{3}-10.4x^{2}+72.96x$$

Combine 2x^{3} and -2x^{3} to get 0.

$$-8x+10.4x^{2}-41.6-10.4x^{2}+72.96x$$

Combine 10.4x^{2} and -10.4x^{2} to get 0.

$$-8x-41.6+72.96x$$

Combine -8x and 72.96x to get 64.96x.

$$64.96x-41.6$$

Expand

$$\frac{1624x}{25}-41.6$$

Solution Steps

Use the distributive property to multiply 2 by x+5.2.

$$\left(2x+10.4\right)\left(x^{2}-4\right)-x\left(\left(x+5.2\right)^{2}+x^{2}-100\right)$$

Use the distributive property to multiply 2x+10.4 by x^{2}-4.

$$2x^{3}-8x+10.4x^{2}-41.6-x\left(\left(x+5.2\right)^{2}+x^{2}-100\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5.2\right)^{2}.

$$2x^{3}-8x+10.4x^{2}-41.6-x\left(x^{2}+10.4x+27.04+x^{2}-100\right)$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{3}-8x+10.4x^{2}-41.6-x\left(2x^{2}+10.4x+27.04-100\right)$$

Subtract 100 from 27.04 to get -72.96.

$$2x^{3}-8x+10.4x^{2}-41.6-x\left(2x^{2}+10.4x-72.96\right)$$

Use the distributive property to multiply x by 2x^{2}+10.4x-72.96.

$$2x^{3}-8x+10.4x^{2}-41.6-\left(2x^{3}+10.4x^{2}-72.96x\right)$$

To find the opposite of 2x^{3}+10.4x^{2}-72.96x, find the opposite of each term.

$$2x^{3}-8x+10.4x^{2}-41.6-2x^{3}-10.4x^{2}+72.96x$$

Combine 2x^{3} and -2x^{3} to get 0.

$$-8x+10.4x^{2}-41.6-10.4x^{2}+72.96x$$

Combine 10.4x^{2} and -10.4x^{2} to get 0.

$$-8x-41.6+72.96x$$

Combine -8x and 72.96x to get 64.96x.

$$64.96x-41.6$$