Question

Find each of the following products:

(i) (x – 4)(x – 4)

(ii) (2x – 3y)(2x – 3y)

(iii) (3/4 x - 5/6y)(3/4x - 5/6y)

(iv) (x - 3/x)(x - 3/x)

(v) (1/3x² - 9)(1/3x² - 9)

(vi) (1/2y² - 1/3y)(1/2y² - 1/3y)

Answer 1

(i) Given,

(x – 4)(x – 4)

By using the formula (a – b)² = a² – 2ab + b²

We get;

= (x – 4)²

= (x)² – 2 × (x) × 4 + (4)²

= x² – 8x + 16

(ii) Given,

(2x – 3y)(2x – 3y)

By using the formula (a – b)² = a² – 2ab + b²

We get;

= (2x – 3y)²

= (2x)² – 2 × (2x) × (3y) + (3y)²

= 4x² – 12xy + 9y²

(iii) \((\frac{3}{4}\text{x} - \frac{5}{6}y)(\frac{3}{4}\text{x}-\frac{5}{6}y)\)

By using the formula (a – b)² = a² – 2ab + b²

We get;

(iv) \((\text{x}-\frac{3}{\text{x}})(\text{x}-\frac{3}{\text{x}})\)

By using the formula (a – b)² = a² – 2ab + b²

We get;

(v) \((\frac{1}{3}\text{x}^2-9)(\frac{1}{3}\text{x}^{2}-9)\)

By using the formula (a – b)² = a² – 2ab + b²

We get;

(vi) \((\frac{1}{2}y^2-\frac{1}{3}y)(\frac{1}{2}y^2-\frac{1}{3}y)\)