Question 3Factorise the following using appropriate identities:(i) 9x2 + 6xy + y2(ii) 4y2 - 4y + 1(iii) x2−(y2100)x^2 - \Big(\dfrac{y^2}{100}\Big)x2−(100y2)

Question

Question 3Factorise the following using appropriate identities:(i) 9x2 + 6xy + y2(ii) 4y2 - 4y + 1(iii) x2−(y2100)x^2 - \Big(\dfrac{y^2}{100}\Big)x2−(100y2​)

Accepted Answer

(i) 9x2 + 6xy + y2[∵ a2 + 2ab + b2 = (a + b)2]= (3x)2 + 2(3x)(y) + (y)2= (3x + y)2Hence, 9x2 + 6xy + y2 = (3x + y)(3x + y)(ii) 4y2 - 4y + 1[∵ a2 - 2ab + b2 = (a - b)2]= (2y)2 - 2(2y)(1) + (1)2= (2y - 1)2Hence, 4y2 - 4y + 1 = (2y - 1)(2y - 1)(iii) x2−(y2100)x^2 - \Big(\dfrac{y^2}{100}\Big)x2−(100y2​)[∵ a2 - b2 = (a - b)(a + b)]x2−(y2100)=x2−(y10)2=(x−y10)(x+y10)x^2 - \Big(\dfrac{y^2}{100}\Big) \[1em] = x^2 - \Big(\dfrac{y}{10}\Big)^2 \[1em] = \Big(x - \dfrac{y}{10}\Big) \Big(x + \dfrac{y}{10}\Big)x2−(100y2​)=x2−(10y​)2=(x−10y​)(x+10y​)Hence, x2−(y2100)x^2 - \Big(\dfrac{y^2}{100}\Big)x2−(100y2​) = (x−y10)(x+y10)\Big(x - \dfrac{y}{10}\Big) \Big(x + \dfrac{y}{10}\Big)(x−10y​)(x+10y​)

Polynomials — Question 3

Question 3