Solve (9a-1/2b)(5a+1/4b)

$$( 9 a - \frac { 1 } { 2 } b ) ( 5 a + \frac { 1 } { 4 } b )$$

Evaluate

$$\frac{\left(18a-b\right)\left(20a+b\right)}{8}$$

Solution Steps

Apply the distributive property by multiplying each term of 9a-\frac{1}{2}b by each term of 5a+\frac{1}{4}b.

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

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

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

Multiply 9 and \frac{1}{4} to get \frac{9}{4}.

$$45a^{2}+\frac{9}{4}ab-\frac{1}{2}b\times 5a-\frac{1}{2}b^{2}\times \frac{1}{4}$$

Express -\frac{1}{2}\times 5 as a single fraction.

$$45a^{2}+\frac{9}{4}ab+\frac{-5}{2}ba-\frac{1}{2}b^{2}\times \frac{1}{4}$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$45a^{2}+\frac{9}{4}ab-\frac{5}{2}ba-\frac{1}{2}b^{2}\times \frac{1}{4}$$

Combine \frac{9}{4}ab and -\frac{5}{2}ba to get -\frac{1}{4}ab.

$$45a^{2}-\frac{1}{4}ab-\frac{1}{2}b^{2}\times \frac{1}{4}$$

Multiply -\frac{1}{2} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$45a^{2}-\frac{1}{4}ab+\frac{-1}{2\times 4}b^{2}$$

Do the multiplications in the fraction \frac{-1}{2\times 4}.

$$45a^{2}-\frac{1}{4}ab+\frac{-1}{8}b^{2}$$

Fraction \frac{-1}{8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$45a^{2}-\frac{1}{4}ab-\frac{1}{8}b^{2}$$

Expand

$$-\frac{ab}{4}-\frac{b^{2}}{8}+45a^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 9a-\frac{1}{2}b by each term of 5a+\frac{1}{4}b.

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

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

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

Multiply 9 and \frac{1}{4} to get \frac{9}{4}.

$$45a^{2}+\frac{9}{4}ab-\frac{1}{2}b\times 5a-\frac{1}{2}b^{2}\times \frac{1}{4}$$

Express -\frac{1}{2}\times 5 as a single fraction.

$$45a^{2}+\frac{9}{4}ab+\frac{-5}{2}ba-\frac{1}{2}b^{2}\times \frac{1}{4}$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$45a^{2}+\frac{9}{4}ab-\frac{5}{2}ba-\frac{1}{2}b^{2}\times \frac{1}{4}$$

Combine \frac{9}{4}ab and -\frac{5}{2}ba to get -\frac{1}{4}ab.

$$45a^{2}-\frac{1}{4}ab-\frac{1}{2}b^{2}\times \frac{1}{4}$$

Multiply -\frac{1}{2} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$45a^{2}-\frac{1}{4}ab+\frac{-1}{2\times 4}b^{2}$$

Do the multiplications in the fraction \frac{-1}{2\times 4}.

$$45a^{2}-\frac{1}{4}ab+\frac{-1}{8}b^{2}$$

Fraction \frac{-1}{8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$45a^{2}-\frac{1}{4}ab-\frac{1}{8}b^{2}$$