Find each of the following products:(i) (x + 3)(x – 3) (ii) (2x + 5

1.	Find each of the following products:(i) (x + 3)(x – 3) (ii) (2x + 5)(2x – 5) (iii) (8 + x)(8 – x) (iv) (7x + 11y)(7x – 11y)
Answer» (i) Given, (x + 3)(x – 3) By using the formula (a + b) (a – b) = a² – b² We get; = x(x + 3) – 3(x + 3) = x² + 3x – 3x – 9 = x² – 9 (ii) Given, (2x + 5)(2x – 5) By using the formula (a + b) (a – b) = a² – b² We get; = 2x(2x + 5) – 5(2x + 5) = 4x² + 10x – 10x – 25 = 4x² – 25 (iii) Given, (8 + x)(8 – x) By using the formula (a + b) (a – b) = a² – b² We get; = 8(8 + x) – x(8 + x) = 64 + 8x – 8x – x² = 64 – x² (iv) Given, (7x + 11y)(7x – 11y) By using the formula (a + b) (a – b) = a² – b² We get; = 7x(7x + 11y) – 11y(7x + 11y) = 49x² + 77xy – 77xy – 121y² = 49x² – 121y²

Find each of the following products:(i) (x + 3)(x – 3) (ii) (2x + 5)(2x – 5) (iii) (8 + x)(8 – x) (iv) (7x + 11y)(7x – 11y)

Answer»

(i) Given,

(x + 3)(x – 3)

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

We get;

= x(x + 3) – 3(x + 3)

= x² + 3x – 3x – 9

= x² – 9

(ii) Given,

(2x + 5)(2x – 5)

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

We get;

= 2x(2x + 5) – 5(2x + 5)

= 4x² + 10x – 10x – 25

= 4x² – 25

(iii) Given,

(8 + x)(8 – x)

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

We get;

= 8(8 + x) – x(8 + x)

= 64 + 8x – 8x – x²

= 64 – x²

(iv) Given,

(7x + 11y)(7x – 11y)

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

We get;

= 7x(7x + 11y) – 11y(7x + 11y)

= 49x² + 77xy – 77xy – 121y²

= 49x² – 121y²