Question

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) (1/4a-1/2b+1)^2
PLEASE ANSWER ALL THESE QUESTIONS PLEASE PLEASE​

Answer 1

Answer:

Step-by-step explanation:

i) (x + 2y + 4z)2 (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca (x + 2y + 4z)2 =(x)2 + (2y)2 + (4z)2 + 2(x)(2y) + 2(2y)(4z) + 2(4z)(x) = x2 + 4y2 + 16z2 + 4xy + 16yz + 8zx

ii) (2x – y + z)2 (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx (2x – y + z)2= (2x)2 + (-y)2 + (z)2 + 2(2x)(-y) + 2(-y)(z) + 2(z)(2x) = 4x2 + y2 + z2 – 4xy – 2yz + 4zx.

(iii) (-2x + 3y + 2z)2 (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx (-2x + 3y + 2z)2 = (-2x)2 + (3y)22 + (2z)2 + 2(-2x)(3y) + 2(3y)(2z) + 2(2z)(-2x) = 4x2 + 9x2 + 4z2 – 12xy + 12yz – 8zx

(iv) (3a – 7b – c)2 (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca (3a – 7b – c)2 =(3a)2 + (-7b)2 + (-c)2 + 2(3a)(-7b) + 2(-7b)(-c) + 2(-c)(3a) = 9a2 + 49b2 + c2 – 42ab – 14bc – 6ca.

(v) (-2x + 5y – 3z)2 (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx (-2x + 5y – 3z)2 = (-2x)2 + (5y)2 + (-3z)2 + 2(-2x)(5y) + 2(5y)(-3z) + 2(-3z)(-2x) = 4x2 + 25y2 + 9z2 – 20xy – 30yz