Solve (1/2y+5)(1/2y-9)

$$( \frac{ 1 }{ 2 } y+5)( \frac{ 1 }{ 2 } y-9)$$

Evaluate

$$\frac{\left(y-18\right)\left(y+10\right)}{4}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{1}{2}y+5 by each term of \frac{1}{2}y-9.

$$\frac{1}{2}y\times \frac{1}{2}y+\frac{1}{2}y\left(-9\right)+5\times \frac{1}{2}y-45$$

Multiply y and y to get y^{2}.

$$\frac{1}{2}y^{2}\times \frac{1}{2}+\frac{1}{2}y\left(-9\right)+5\times \frac{1}{2}y-45$$

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

$$\frac{1\times 1}{2\times 2}y^{2}+\frac{1}{2}y\left(-9\right)+5\times \frac{1}{2}y-45$$

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

$$\frac{1}{4}y^{2}+\frac{1}{2}y\left(-9\right)+5\times \frac{1}{2}y-45$$

Multiply \frac{1}{2} and -9 to get \frac{-9}{2}.

$$\frac{1}{4}y^{2}+\frac{-9}{2}y+5\times \frac{1}{2}y-45$$

Fraction \frac{-9}{2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$\frac{1}{4}y^{2}-\frac{9}{2}y+5\times \frac{1}{2}y-45$$

Multiply 5 and \frac{1}{2} to get \frac{5}{2}.

$$\frac{1}{4}y^{2}-\frac{9}{2}y+\frac{5}{2}y-45$$

Combine -\frac{9}{2}y and \frac{5}{2}y to get -2y.

$$\frac{1}{4}y^{2}-2y-45$$

Expand

$$\frac{y^{2}}{4}-2y-45$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{1}{2}y+5 by each term of \frac{1}{2}y-9.

$$\frac{1}{2}y\times \frac{1}{2}y+\frac{1}{2}y\left(-9\right)+5\times \frac{1}{2}y-45$$

Multiply y and y to get y^{2}.

$$\frac{1}{2}y^{2}\times \frac{1}{2}+\frac{1}{2}y\left(-9\right)+5\times \frac{1}{2}y-45$$

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

$$\frac{1\times 1}{2\times 2}y^{2}+\frac{1}{2}y\left(-9\right)+5\times \frac{1}{2}y-45$$

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

$$\frac{1}{4}y^{2}+\frac{1}{2}y\left(-9\right)+5\times \frac{1}{2}y-45$$

Multiply \frac{1}{2} and -9 to get \frac{-9}{2}.

$$\frac{1}{4}y^{2}+\frac{-9}{2}y+5\times \frac{1}{2}y-45$$

Fraction \frac{-9}{2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$\frac{1}{4}y^{2}-\frac{9}{2}y+5\times \frac{1}{2}y-45$$

Multiply 5 and \frac{1}{2} to get \frac{5}{2}.

$$\frac{1}{4}y^{2}-\frac{9}{2}y+\frac{5}{2}y-45$$

Combine -\frac{9}{2}y and \frac{5}{2}y to get -2y.

$$\frac{1}{4}y^{2}-2y-45$$