Question

Use the formula to multiply the following.

(i) (x + y) (x $-$y) (ii) (3x$-$5) (3x + 5) (iii) (a + 6) (a $-$6) (iv) $\left(\frac{x}{5}+6\right)\left(\frac{x}{5}-6\right)$

Answer 1

It is known that, (a + b) (a − b) = a² − b².
$$\begin{gathered} \left(\mathrm{i}\right)\left(x+y\right)\left(x-y\right) \\ ={\left(x\right)}^2-{\left(y\right)}^2 \\ =x^2-y^2 \end{gathered}$$
$$\begin{gathered} \left(\mathrm{ii}\right)\left(3x-5\right)\left(3x+5\right) \\ ={\left(3x\right)}^2-{\left(5\right)}^2 \\ =9x^2-25 \end{gathered}$$
$$\begin{gathered} \left(\mathrm{iii}\right)\left(a+6\right)\left(a-6\right) \\ ={\left(a\right)}^2-{\left(6\right)}^2 \\ =a^2-36 \end{gathered}$$
$$\begin{gathered} \left(\mathrm{iv}\right)\left(\frac{x}{5}+6\right)\left(\frac{x}{5}-6\right) \\ ={\left(\frac{x}{5}\right)}^2-{\left(6\right)}^2 \\ =\frac{x^2}{25}-36 \end{gathered}$$