Solve (3/4a-1)*(-1-3/4a)=

$$( \frac { 3 } { 4 } a - 1 ) \cdot ( - 1 - \frac { 3 } { 4 } a ) =$$

Evaluate

$$-\frac{9a^{2}}{16}+1$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(-1\right)^{2}-\left(\frac{3}{4}a\right)^{2}$$

Calculate -1 to the power of 2 and get 1.

$$1-\left(\frac{3}{4}a\right)^{2}$$

Expand \left(\frac{3}{4}a\right)^{2}.

$$1-\left(\frac{3}{4}\right)^{2}a^{2}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$1-\frac{9}{16}a^{2}$$

Expand

$$-\frac{9a^{2}}{16}+1$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(-1\right)^{2}-\left(\frac{3}{4}a\right)^{2}$$

Calculate -1 to the power of 2 and get 1.

$$1-\left(\frac{3}{4}a\right)^{2}$$

Expand \left(\frac{3}{4}a\right)^{2}.

$$1-\left(\frac{3}{4}\right)^{2}a^{2}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$1-\frac{9}{16}a^{2}$$