Question

35. Factorise each of the following:
(i) 16x2 + 4y2 + 9z2 - 16xy - 12yz + 24xz
[NCERT Exemplar Problems)​

Answer 1

Answer:

Now as the term looks familiar to a formula studied by me in class 9th as far as I remembered

(a+b+c)²=a²+b²+c²+2(ab+bc+ca)

so here a=4x , b=minus(-) 2y and c=3z

Now by applying the formula

(4x)²+(-2y)²+(3z)²+2(4x×3z+-2y×3z+4x×-2y) so

it is (4x-2y+3z)²

Answer 2

Answer:

16x

2

+4y

2

+9z

2

16xy+12yz+24xz

Using (a+b+c)

2

=a

2

+b

2

+c

2

+2ab+2bc+2ac

=(4x)

2

+(2y)

2

+(3z)

2

+2(4x)(2y)+2(2y)(3z)+2(4x)(3z)

=(4x+2y+3z)(4x+2y+3z)