Solve (1/7-y)(1/2-y)=

$$( \frac { 1 } { 7 } - y ) ( \frac { 1 } { 2 } - y ) =$$

Evaluate

$$y^{2}-\frac{9y}{14}+\frac{1}{14}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{1}{7}-y by each term of \frac{1}{2}-y.

$$\frac{1}{7}\times \frac{1}{2}+\frac{1}{7}\left(-1\right)y-y\times \frac{1}{2}+y^{2}$$

Multiply \frac{1}{7} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{7\times 2}+\frac{1}{7}\left(-1\right)y-y\times \frac{1}{2}+y^{2}$$

Do the multiplications in the fraction \frac{1\times 1}{7\times 2}.

$$\frac{1}{14}+\frac{1}{7}\left(-1\right)y-y\times \frac{1}{2}+y^{2}$$

Multiply \frac{1}{7} and -1 to get -\frac{1}{7}.

$$\frac{1}{14}-\frac{1}{7}y-y\times \frac{1}{2}+y^{2}$$

Multiply -1 and \frac{1}{2} to get -\frac{1}{2}.

$$\frac{1}{14}-\frac{1}{7}y-\frac{1}{2}y+y^{2}$$

Combine -\frac{1}{7}y and -\frac{1}{2}y to get -\frac{9}{14}y.

$$\frac{1}{14}-\frac{9}{14}y+y^{2}$$

Expand

$$y^{2}-\frac{9y}{14}+\frac{1}{14}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{1}{7}-y by each term of \frac{1}{2}-y.

$$\frac{1}{7}\times \frac{1}{2}+\frac{1}{7}\left(-1\right)y-y\times \frac{1}{2}+y^{2}$$

Multiply \frac{1}{7} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{7\times 2}+\frac{1}{7}\left(-1\right)y-y\times \frac{1}{2}+y^{2}$$

Do the multiplications in the fraction \frac{1\times 1}{7\times 2}.

$$\frac{1}{14}+\frac{1}{7}\left(-1\right)y-y\times \frac{1}{2}+y^{2}$$

Multiply \frac{1}{7} and -1 to get -\frac{1}{7}.

$$\frac{1}{14}-\frac{1}{7}y-y\times \frac{1}{2}+y^{2}$$

Multiply -1 and \frac{1}{2} to get -\frac{1}{2}.

$$\frac{1}{14}-\frac{1}{7}y-\frac{1}{2}y+y^{2}$$

Combine -\frac{1}{7}y and -\frac{1}{2}y to get -\frac{9}{14}y.

$$\frac{1}{14}-\frac{9}{14}y+y^{2}$$