Solve (2.5p-1.5q)^2-(1.5p-2)

$$( 2.5 p - 1.5 q ) ^ { 2 } - ( 1.5 p - 2 )$$

Evaluate

$$\left(\frac{5p-3q}{2}\right)^{2}-\frac{3p}{2}+2$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2.5p-1.5q\right)^{2}.

$$6.25p^{2}-7.5pq+2.25q^{2}-\left(1.5p-2\right)$$

To find the opposite of 1.5p-2, find the opposite of each term.

$$6.25p^{2}-7.5pq+2.25q^{2}-1.5p+2$$

Expand

$$-\frac{15pq}{2}+\frac{9q^{2}}{4}+\frac{25p^{2}}{4}-\frac{3p}{2}+2$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2.5p-1.5q\right)^{2}.

$$6.25p^{2}-7.5pq+2.25q^{2}-\left(1.5p-2\right)$$

To find the opposite of 1.5p-2, find the opposite of each term.

$$6.25p^{2}-7.5pq+2.25q^{2}-1.5p+2$$