(a+b+c)2= a2+b2+c2+2ab+2bc+2ca
Problem 1 :
Expand (x+y+z)²
(A) (x²+y²+z²+2xy+2yz+2zx)
(B) (x²+y2 + z²+2xy-2yz-2zx)
(C) (x²+y²-z²-2xy+2yz+2zx)
Problem 2 :
Expand (2a+b+c)²
(A) (4a²-b²-c²-4ab+2bc+4ca)
(B) (4a²-b²+c²+4ab-2bc-4ca)
(C) (4a²+b²+c²+4ab+2bc+4ca)
Problem 3 :
Expand (2a-b-c)²
(A) (4a²-b²-c²-4ab+2bc+4ca)
(B) (4a²-b²+c²+4ab-2bc-4ca)
(C) (4a²+b²+c²-4ab+2bc-4ca)
Problem 4 :
Expand (2a+3b+4c)²
(A) 4a²+9b²+16c²+12ab+24bc+16ca
(B) 4a²-9b²+16c²-12ab+24bc+16ca
(C) 9a²+9b²+16c²+24ab+12bc+16ca
Problem 5 :
Expand (3p-2r+s)²
(A) 9p²-4r²-s²-12pr-4rs+6st
(B) 9p²+r²+s²-12pr+4rs-6st
(C) 9p²+4r²+s²-12pr-4rs+6sp
Problem 6 :
Expand (p+3q+s)²
(A) p²-9q²+s²+6pq-6qs+2sp
(B) p²+9q²+s²+6pq+6qs+2sp
(C) p²-9q²+s²+6pq-6qs-2sp
Problem 1 :
Expand (x+y+z)²
Solution :
a = x, b = y and c = z
(x+y+z)2 = x2+y2+z2+2xy+2yz+2zx
Problem 2 :
Expand (2a+b+c)²
Solution :
a = 2a, b = b and c = c
(2a+b+c)² = (2a)2+b2+c2+2(2a)(b)+2bc+2c(2a)
= 4a2+b2+c2+4ab+2bc+4ca
Problem 3 :
Expand (2a-b-c)²
Solution :
a = 2a, b = -b and c = -c
(2a-b-c)² = (2a)2+b2+c2+2(2a)(-b)+2(-b)(-c)+2(-c)(2a)
= 4a2+b2+c2-4ab-2bc-4ca
Problem 4 :
Expand (2a + 3b + 4c)²
Solution :
a = 2a, b = 3b and c = 4c
= (2a)2+(3b)2+(4c)2+2(2a)(3b)+2(3b)(4c)+2(4c)(2a)
= 4a2+9b2+16c2+12ab+24bc+16ca
Problem 5 :
Expand (3p-2r+s)²
Solution :
a = 3p, b = -2r and c = s
= (3p)2+(-2r)2+s2+2(3p)(-2r)+2(-2r)s+2s(3p)
= 9p2+4r2+s2-12pr-4rs+6sp
Problem 6 :
Expand (p+3q+s)²
Solution :
a = p, b = 3q and c = s
= p2+(3q)2+s2+2(p)(3q)+2(3q)s+2s(p)
= p2+9q2+s2+6pq+6qs+2sp
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