PRACTICE QUESTIONS FOR a PLUS b PLUS c WHOLE SQUARE

(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

Solutions for Practice Questions

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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