Question

Expand.
(1) (5x − 7) (5x − 9)
(2) (2x − 3y)³
(3) (a + $\frac{1}{2}$)³

Answer 1

(1) (5x − 7) (5x − 9)

$$\begin{gathered} =5x\left(5x-9\right)-7\left(5x-9\right) \\ =25x^2-45x-35x+63 \\ =25x^2-80x+63 \end{gathered}$$

(2) (2x − 3y)³

$$\begin{gathered} \mathrm{Using}\mathrm{identity}:{\left(a-b\right)}^3=a^3-b^3-3a^{2}b+3a{b}^2,\mathrm{we}\mathrm{get} \\ {\left(2x\right)}^3-{\left(3y\right)}^3-3{\left(2x\right)}^2\left(3y\right)+3\left(2x\right){\left(3y\right)}^2 \\ =8x^3-27y^3-36x^{2}y+54x{y}^2 \end{gathered}$$

(3) (a + $\frac{1}{2}$)³

$$\begin{gathered} \mathrm{Using}\mathrm{identity}:{\left(a+b\right)}^3=a^3+b^3+3a^{2}b+3a{b}^2,\mathrm{we}\mathrm{get} \\ {\left(a\right)}^3+{\left(\frac{1}{2}\right)}^3+3{\left(a\right)}^2\left(\frac{1}{2}\right)+3\left(a\right){\left(\frac{1}{2}\right)}^2 \\ =a^3+\frac{1}{8}+\frac{3}{2}{a}^2+\frac{3}{4}a \end{gathered}$$