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