Question

Find each of the following products:

(i) (5x² + 3/4y²)(5x² - 3/4y²)

(ii) (4x/5 - 5y/3)(4x/5 + 5y/3)

(iii) (x + 1/x)(x - 1/x)

(iv) (1/x + 1/y)(1/x - 1/y)

(v) (2a + 3/b)(2a - 3/b)

Answer 1

(i) Given,

By using the formula (a + b) (a – b) = a² – b²

We get;

(ii) \((\frac{4\text{x}}{5}-\frac{5y}{3})(\frac{4\text{x}}{5}+\frac{5y}{3})\)

By using the formula (a + b) (a – b) = a² – b²

We get;

(iii) \((\text{x}+\frac{1}{\text{x}})(\text{x}-\frac{1}{\text{x}})\)

By using the formula (a + b) (a – b) = a² – b²

We get;

= \(\text{x}^2-\frac{1}{\text{x}}^2\)

(iv) \((\frac{1}{\text{x}}+\frac{1}{y})(\frac{1}{\text{x}}-\frac{1}{y})\)

By using the formula (a + b) (a – b) = a² – b²

We get;

= \(\frac{1}{\text{x}^{2}}-\frac{1}{y^2}\)

 (v) \((2a+\frac{3}{b})(2a\,-\frac{3}{b})\)

By using the formula (a + b) (a – b) = a² – b²

We get;

\(=4a^2-\frac{9}{b^2}\)