Question

"Question 4 Expand each of the following, using suitable identities:
(i) (x+2y+4z)^2
(ii) (2x - y + z)^2
(iii) (-2x+3y+2z)^2
(iv) (3a-7b-c)^2
(v) (-2x+5y-3z)^2
(vi) [a/4 - b/2 + 1]^2

Class 9 - Math - Polynomials Page 49"

Answer 1

It is known that,

(x+y+z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx

(i) (x+2y+4z)2 = x2+(2y)2 +(4z)2 + 2(x)(2y)+2(2y)(4z)+2(4z)(x)

=x2+4y2+16z2+4xy+16yz+8xz

(ii) (2x−y+z)2=(2x)2+(−y)2+(z)2+2(2x)(−y)+2(−y)(z)+2(z)(2x)

=4x2+y2+z2−4xy−2yz+4xz

(iii) (−2x+3y+2z)2

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

=4x2+9y2+4z2−12xy+12yz−8xz

(iv) (3a−7b−c)2

=(3a)2+(−7b)2+(−c)2+2(3a)( −7b)+2(−7b)( −c)+2(−c)(3a)

=9a2+49b2+c2−42ab+14bc−6ac

(v) (−2x+5y−3z)2

=(−2x)2+(5y)2+(−3z)2+2(−2x)(5y)+2(5y)( −3z)+2(−3z)( −2x)

=4x2+25y2+9z2−20xy−30yz+12xz