#### Chapter 4 Algebraic Identities R.D. Sharma Solutions for Class 9th Math Exercise 4.2

Exercise 4.2

1. Write the following in the expanded form:
(i) (a +2b + c)2
(ii) (2a − 3b − c)2
(iii) (−3x + y + z)2
(iv) (m + 2n − 5p)2
(v) (2 + x − 2y)2
(vi) (a2 + b2 + c2)2
(vii) (ab + bc + ca)2
(viii) (xy+yz+zx)2
(ix) (abc+bca+cab)2
(x) (x+2y+4z)2
(xi) (2x − y + z)2
(xii) (−2x + 3y + 2z)2

Solution

2.Simplify:
(i) (a +b + c)2 + (a − b + c)2
(ii) (a +b + c)2 − (a − b + c)2
(iii) (a +b + c)+ (a − b + c)2 + (a +b − c)2
(iv) (2x + p − c)− (2x − p + c)2
(v) (x2 + y− z2) − (x2 − y2 + z2)2

Solution

3. If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.

Solution

4. If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c.

Solution

5.  If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 c2.

Solution

6.  Find the value of 4x2 + y2 + 25x+ 4xy − 10yz − 20zx when x= 4, y = 3 and z = 2.

Solution

7. Simplify each of the following expressions:
(i) (x+y+z)2+(x+y2+z3)2(x2+y3+z4)2
(ii) (x + y− 2z)2 − x2 − y2 − 3z2 + 4xy
(iii) (x2− x + 1)2 − (x2 + x + 1)2

Solution