Question

Use suitable identities to find the following products:

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

(ii) (x + 8) (x – 10)

(iii) (3x + 4) (3x – 5)

(iv) $(y^ 2 + \frac{3 }{ 2}) (y^ 2 – \frac{3 }{ 2})$

(v) (3 – 2x) (3 + 2x)

Answer 1

(i) (x + 4)(x + 10) : By using the identity (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) : By using the identity (x + a) (x + b) = x2 + (a + b)x + ab

(x+8) (x-10) = x2 + (x - 10)x + (8)(-10) = x2 - 2x - 80

**(iii) (3x + 4)(3x - 5): ** 9(x + $\frac{4 }{ 3}$)(x - $\frac{5 }{ 3}$) By using the identity (x + a) (x + b) = x2 + (a + b)x + ab

9(x + $\frac{4 }{ 3}$)(x - $\frac{5 }{ 3}$) = 9[x2 + ($\frac{4 }{ 3}$ - $\frac{4 }{ 3}$)x + ($\frac{4 }{ 3}$)(-$\frac{5}{ 3}$)]

= 9[x2 - $\frac{1 }{ 3}$x - $\frac{20 }{ 9}$] = 9x2 - 3x - 20

(iv) (y2 + $\frac{3 }{2}$)(y2 - $\frac{3 }{ 2}$) : By using the identity (x + y) (x - y) = x2 - y2

(y2 + $\frac{3 }{ 2}$) (y2 - $\frac{3 }{ 2}$) = (y2)2 - ($\frac{3 }{ 2}$)2

= y4 - $\frac{9 }{ 4}$

(v) (3 - 2x)(3 + 2x) : By using the identity (x + y) (x - y) = x2 - y2

(3 - 2x) (3 + 2x) = (3)2 - (2x)2

= 9 - 4x2