Factorise the following using appropriate identities: (i) 9x 2 + 6xy + y 2 (ii) 4y 2 – 4y + 1 (iii) x 2 – $\frac{y^2 }{ 100}$

Question

Factorise the following using appropriate identities:  (i) 9x 2 + 6xy + y 2  (ii) 4y 2 – 4y + 1  (iii) x 2 –  $\frac{y^2 }{ 100}$

cdquestions Admin · Accepted Answer

(i) 9x 2 + 6xy + y 2 = (3x) 2 + 2(3x)(y)+(y )2   = (3x + y)(3x + y)     [x 2 + 2xy + y 2 = (x + y) 2 ] (ii) 4y 2 - 4y + 1 = (2y) 2 - 2(2y)91) + (1) 2   = (2y - 1)(2y - 1)      [x 2 - 2xy + y 2 = (x - y) 2 ] (iii) x 2 - $\frac{y^2 }{ 100}$  = x2 - ( $\frac{y }{ 10}$ ) 2   = (x +  $\frac{y }{ 10}$ ) (x - $\frac{y }{ 10}$ )     [x 2 - y 2 = (x + y) (x - y)]

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Factorise the following using appropriate identities:
(i) 9x²+ 6xy + y2
(ii) 4y² – 4y + 1
(iii) x² – \(\frac{y^2 }{ 100}\)

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions

Factorise the following using appropriate identities: (i) 9x 2 + 6xy + y 2 (ii) 4y 2 – 4y + 1 (iii) x 2 – \(\frac{y^2 }{ 100}\)

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions

Factorise the following using appropriate identities:
(i) 9x²+ 6xy + y2
(ii) 4y² – 4y + 1
(iii) x² – \(\frac{y^2 }{ 100}\)