Use suitable identities to find the following products :(i) (x + 4) (x

1.	Use suitable identities to find the following products :(i) (x + 4) (x + 10) (ii) (x + 8) (x – 10) (iii) (3x + 4) (3x – 5) (iv) (y2 + \(\frac{3}{2}\))(y2 - \(\frac{3}{2}\))(v) (3 – 2x) (3 + 2x)
Answer» (i) (x + 4) (x + 10) Suitable identity is (x + a) (x + b) = x² + (a + b)x + ab (x + 4) (x + 10) = x² + (4 + 10)x + (4 × 10) = x² + 14x + 40 (ii) (x + 8) (x- 10) Suitable identity is (x + a) (x + b) = x² + (a + b)x + ab (x + 8) (x – 10) = (x)² + (8 – 10)x + (8 × -10) = x² + (-2)x + (-80) = x² – 2x – 80 (iii) (3x + 4) (3x – 5) Suitable identity is (x + a) (x + b) = x²+ (a + b)x + ab (3x + 4) (3x – 5) = (3x)² + (+4 – 5)3x + (4 x -5) = 9x² + (-1)3x + (-20) = 9x² – 3x – 20 (iv) Suitable identity is (a + b) (a – b) = a² – b² (v) (3 – 2x) (3 + 2x) Suitable identity is (a + b) (a – b) = a² – b² (3 – 2x) (3 + 2x) = (3)² – (2x)² = 9 – 4x² .

Use suitable identities to find the following products :(i) (x + 4) (x + 10) (ii) (x + 8) (x – 10) (iii) (3x + 4) (3x – 5) (iv) (y2 + \(\frac{3}{2}\))(y2 - \(\frac{3}{2}\))(v) (3 – 2x) (3 + 2x)

Answer»

(i) (x + 4) (x + 10)

Suitable identity is (x + a) (x + b)

= x² + (a + b)x + ab (x + 4) (x + 10)

= x² + (4 + 10)x + (4 × 10)

= x² + 14x + 40

(ii) (x + 8) (x- 10)

Suitable identity is (x + a) (x + b)

= x² + (a + b)x + ab (x + 8) (x – 10)

= (x)² + (8 – 10)x + (8 × -10)

= x² + (-2)x + (-80)

= x² – 2x – 80

(iii) (3x + 4) (3x – 5)

Suitable identity is (x + a) (x + b)

= x²+ (a + b)x + ab (3x + 4) (3x – 5)

= (3x)² + (+4 – 5)3x + (4 x -5)

= 9x² + (-1)3x + (-20)

= 9x² – 3x – 20

(iv) Suitable identity is (a + b) (a – b)

= a² – b²

(v) (3 – 2x) (3 + 2x)

Suitable identity is (a + b) (a – b)

= a² – b² (3 – 2x) (3 + 2x)

= (3)² – (2x)² = 9 – 4x² .