Solve 1300.5*(x^2-10.5x+27.56)-2704*(x^2-10.4x+27.03)+4404.5*(x^2-10.3x+26.52)

$$1300.5 \times ( { x }^{ 2 } -10.5x+27.56)-2704 \times ( { x }^{ 2 } -10.4x+27.03)+4404.5 \times ( { x }^{ 2 } -10.3x+26.52)$$

Evaluate

$$3001x^{2}-30900x+79560$$

Solution Steps

Use the distributive property to multiply 1300.5 by x^{2}-10.5x+27.56.

$$1300.5x^{2}-13655.25x+35841.78-2704\left(x^{2}-10.4x+27.03\right)+4404.5\left(x^{2}-10.3x+26.52\right)$$

Use the distributive property to multiply -2704 by x^{2}-10.4x+27.03.

$$1300.5x^{2}-13655.25x+35841.78-2704x^{2}+28121.6x-73089.12+4404.5\left(x^{2}-10.3x+26.52\right)$$

Combine 1300.5x^{2} and -2704x^{2} to get -1403.5x^{2}.

$$-1403.5x^{2}-13655.25x+35841.78+28121.6x-73089.12+4404.5\left(x^{2}-10.3x+26.52\right)$$

Combine -13655.25x and 28121.6x to get 14466.35x.

$$-1403.5x^{2}+14466.35x+35841.78-73089.12+4404.5\left(x^{2}-10.3x+26.52\right)$$

Subtract 73089.12 from 35841.78 to get -37247.34.

$$-1403.5x^{2}+14466.35x-37247.34+4404.5\left(x^{2}-10.3x+26.52\right)$$

Use the distributive property to multiply 4404.5 by x^{2}-10.3x+26.52.

$$-1403.5x^{2}+14466.35x-37247.34+4404.5x^{2}-45366.35x+116807.34$$

Combine -1403.5x^{2} and 4404.5x^{2} to get 3001x^{2}.

$$3001x^{2}+14466.35x-37247.34-45366.35x+116807.34$$

Combine 14466.35x and -45366.35x to get -30900x.

$$3001x^{2}-30900x-37247.34+116807.34$$

Add -37247.34 and 116807.34 to get 79560.

$$3001x^{2}-30900x+79560$$

Expand

$$3001x^{2}-30900x+79560$$

Solution Steps

Use the distributive property to multiply 1300.5 by x^{2}-10.5x+27.56.

$$1300.5x^{2}-13655.25x+35841.78-2704\left(x^{2}-10.4x+27.03\right)+4404.5\left(x^{2}-10.3x+26.52\right)$$

Use the distributive property to multiply -2704 by x^{2}-10.4x+27.03.

$$1300.5x^{2}-13655.25x+35841.78-2704x^{2}+28121.6x-73089.12+4404.5\left(x^{2}-10.3x+26.52\right)$$

Combine 1300.5x^{2} and -2704x^{2} to get -1403.5x^{2}.

$$-1403.5x^{2}-13655.25x+35841.78+28121.6x-73089.12+4404.5\left(x^{2}-10.3x+26.52\right)$$

Combine -13655.25x and 28121.6x to get 14466.35x.

$$-1403.5x^{2}+14466.35x+35841.78-73089.12+4404.5\left(x^{2}-10.3x+26.52\right)$$

Subtract 73089.12 from 35841.78 to get -37247.34.

$$-1403.5x^{2}+14466.35x-37247.34+4404.5\left(x^{2}-10.3x+26.52\right)$$

Use the distributive property to multiply 4404.5 by x^{2}-10.3x+26.52.

$$-1403.5x^{2}+14466.35x-37247.34+4404.5x^{2}-45366.35x+116807.34$$

Combine -1403.5x^{2} and 4404.5x^{2} to get 3001x^{2}.

$$3001x^{2}+14466.35x-37247.34-45366.35x+116807.34$$

Combine 14466.35x and -45366.35x to get -30900x.

$$3001x^{2}-30900x-37247.34+116807.34$$

Add -37247.34 and 116807.34 to get 79560.

$$3001x^{2}-30900x+79560$$