Solve left(5+9right)left(b+8right)left(b+7right)left(b+5right)+1

$$\left( 5+9 \right) \left( b+8 \right) \left( b+7 \right) \left( b+5 \right) +1$$

Evaluate

$$14\left(b+5\right)\left(b+7\right)\left(b+8\right)+1$$

Solution Steps

Add 5 and 9 to get 14.

$$14\left(b+8\right)\left(b+7\right)\left(b+5\right)+1$$

Use the distributive property to multiply 14 by b+8.

$$\left(14b+112\right)\left(b+7\right)\left(b+5\right)+1$$

Apply the distributive property by multiplying each term of 14b+112 by each term of b+7.

$$\left(14b^{2}+98b+112b+784\right)\left(b+5\right)+1$$

Combine 98b and 112b to get 210b.

$$\left(14b^{2}+210b+784\right)\left(b+5\right)+1$$

Apply the distributive property by multiplying each term of 14b^{2}+210b+784 by each term of b+5.

$$14b^{3}+70b^{2}+210b^{2}+1050b+784b+3920+1$$

Combine 70b^{2} and 210b^{2} to get 280b^{2}.

$$14b^{3}+280b^{2}+1050b+784b+3920+1$$

Combine 1050b and 784b to get 1834b.

$$14b^{3}+280b^{2}+1834b+3920+1$$

Add 3920 and 1 to get 3921.

$$14b^{3}+280b^{2}+1834b+3921$$

Expand

$$14b^{3}+280b^{2}+1834b+3921$$

Solution Steps

Add 5 and 9 to get 14.

$$14\left(b+8\right)\left(b+7\right)\left(b+5\right)+1$$

Use the distributive property to multiply 14 by b+8.

$$\left(14b+112\right)\left(b+7\right)\left(b+5\right)+1$$

Apply the distributive property by multiplying each term of 14b+112 by each term of b+7.

$$\left(14b^{2}+98b+112b+784\right)\left(b+5\right)+1$$

Combine 98b and 112b to get 210b.

$$\left(14b^{2}+210b+784\right)\left(b+5\right)+1$$

Apply the distributive property by multiplying each term of 14b^{2}+210b+784 by each term of b+5.

$$14b^{3}+70b^{2}+210b^{2}+1050b+784b+3920+1$$

Combine 70b^{2} and 210b^{2} to get 280b^{2}.

$$14b^{3}+280b^{2}+1050b+784b+3920+1$$

Combine 1050b and 784b to get 1834b.

$$14b^{3}+280b^{2}+1834b+3920+1$$

Add 3920 and 1 to get 3921.

$$14b^{3}+280b^{2}+1834b+3921$$