Solve 12(y^2+7y+10)div6y+5

$$12 ( y ^ { 2 } + 7 y + 10 ) \div 6 y + 5$$

Evaluate

$$2y\left(y+2\right)\left(y+5\right)+5$$

Short Solution Steps

Use the distributive property to multiply 12 by y^{2}+7y+10.

$$\frac{12y^{2}+84y+120}{6}y+5$$

Express \frac{12y^{2}+84y+120}{6}y as a single fraction.

$$\frac{\left(12y^{2}+84y+120\right)y}{6}+5$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{6}{6}.

$$\frac{\left(12y^{2}+84y+120\right)y}{6}+\frac{5\times 6}{6}$$

Since \frac{\left(12y^{2}+84y+120\right)y}{6} and \frac{5\times 6}{6} have the same denominator, add them by adding their numerators.

$$\frac{\left(12y^{2}+84y+120\right)y+5\times 6}{6}$$

Do the multiplications in \left(12y^{2}+84y+120\right)y+5\times 6.

$$\frac{12y^{3}+84y^{2}+120y+30}{6}$$

Divide each term of 12y^{3}+84y^{2}+120y+30 by 6 to get 2y^{3}+14y^{2}+20y+5.

$$2y^{3}+14y^{2}+20y+5$$

Expand

$$2y^{3}+14y^{2}+20y+5$$

Short Solution Steps

Use the distributive property to multiply 12 by y^{2}+7y+10.

$$\frac{12y^{2}+84y+120}{6}y+5$$

Express \frac{12y^{2}+84y+120}{6}y as a single fraction.

$$\frac{\left(12y^{2}+84y+120\right)y}{6}+5$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{6}{6}.

$$\frac{\left(12y^{2}+84y+120\right)y}{6}+\frac{5\times 6}{6}$$

Since \frac{\left(12y^{2}+84y+120\right)y}{6} and \frac{5\times 6}{6} have the same denominator, add them by adding their numerators.

$$\frac{\left(12y^{2}+84y+120\right)y+5\times 6}{6}$$

Do the multiplications in \left(12y^{2}+84y+120\right)y+5\times 6.

$$\frac{12y^{3}+84y^{2}+120y+30}{6}$$

Divide each term of 12y^{3}+84y^{2}+120y+30 by 6 to get 2y^{3}+14y^{2}+20y+5.

$$2y^{3}+14y^{2}+20y+5$$