Solve 3left(x^4-2x^2+5right)-8left(x^3-4x^2+7xright)

$$3 \left( { x }^{ 4 } -2 { x }^{ 2 } +5 \right) -8 \left( { x }^{ 3 } -4 { x }^{ 2 } +7x \right)$$

Evaluate

$$3x^{4}-8x^{3}+26x^{2}-56x+15$$

Solution Steps

Use the distributive property to multiply 3 by x^{4}-2x^{2}+5.

$$3x^{4}-6x^{2}+15-8\left(x^{3}-4x^{2}+7x\right)$$

Use the distributive property to multiply -8 by x^{3}-4x^{2}+7x.

$$3x^{4}-6x^{2}+15-8x^{3}+32x^{2}-56x$$

Combine -6x^{2} and 32x^{2} to get 26x^{2}.

$$3x^{4}+26x^{2}+15-8x^{3}-56x$$

Expand

$$3x^{4}-8x^{3}+26x^{2}-56x+15$$

Solution Steps

Use the distributive property to multiply 3 by x^{4}-2x^{2}+5.

$$3x^{4}-6x^{2}+15-8\left(x^{3}-4x^{2}+7x\right)$$

Use the distributive property to multiply -8 by x^{3}-4x^{2}+7x.

$$3x^{4}-6x^{2}+15-8x^{3}+32x^{2}-56x$$

Combine -6x^{2} and 32x^{2} to get 26x^{2}.

$$3x^{4}+26x^{2}+15-8x^{3}-56x$$