Addition of Algebraic Expressions
Q1. Find the sum of the following expressions. āĻ¤āĻ˛ā§° ā§°āĻžāĻļāĻŋāĻ¸āĻŽā§āĻšā§° āĻ¯ā§āĻāĻĢāĻ˛ āĻāĻ˛āĻŋāĻ¯āĻŧāĻžāĻāĻ
- 7xy + 5yz - 3zx
- 4yz + 9zx - 4y
- -3xy + 5x - 2xy
Options | āĻŦāĻŋāĻāĻ˛ā§āĻĒāĻ¸āĻŽā§āĻš:
(a) 5x - 4y - 2xy - 9yz + 6zx
(b) 5x - 4y + 6xy + 9yz + 6zx
(c) 5x - 4y + 6xy - 9yz - 6zx
(d) 5x - 4y + 2xy + 9yz + 6zx
Trick : Just combine like terms - āĻāĻā§āĻ§ā§°āĻŖā§° āĻĒāĻĻāĻ¸āĻŽā§āĻš āĻāĻā§āĻ˛āĻā§ āĻ¯ā§āĻ āĻā§°āĻ
(7xy - 3xy - 2xy) + (5yz + 4yz) + (-3zx + 9zx) + (-4y) + (5x)
= 2xy + 9yz + 6zx − 4y + 5x
Re-arrange - āĻĒā§āĻ¨ā§° āĻ¸āĻžāĻāĻŋāĻ˛ā§: 5x - 4y + 2xy + 9yz + 6zx
Ans / āĻāĻ¤ā§āĻ¤ā§°: (d) 5x − 4y + 2xy + 9yz + 6zx
Q2. Subtract 12x - z from the sum of 2x - 3y + 7z and 4z - 5x . Q. 2x−3y+7z āĻā§°ā§ 4z−5x ā§° āĻ¯ā§āĻāĻĢāĻ˛ā§° āĻĒā§°āĻž 12x−z āĻŦāĻŋāĻ¯āĻŧā§āĻ āĻā§°āĻ
Soln
Short Method -
Sum first - āĻĒā§ā§°āĻĨāĻŽā§ āĻ¯ā§āĻ : 2x - 3y + 7z + 4z - 5x = -3x - 3y + 11z
Subtract - āĻŦāĻŋāĻ¯āĻŧā§āĻ -: (12x - z) - (-3x - 3y + 11z)
Change signs after minus - āĻŦāĻŋāĻ¯āĻŧā§āĻā§° āĻĒāĻŋāĻāĻ¤ āĻāĻŋāĻšā§āĻ¨ āĻ¸āĻ˛āĻžāĻāĻ: = 12x - z + 3x + 3y - 11z
Combine like terms - āĻāĻā§āĻ§ā§°āĻŖā§° āĻĒāĻĻ āĻ¯ā§āĻ āĻā§°āĻ:
x : 12x + 3x = 15x
y : 0 + 3y = 3y
z : - z - 11z = −12z
Ans / āĻāĻ¤ā§āĻ¤ā§°: 15x + 3y − 12z
Exam Tip / āĻĒā§°ā§āĻā§āĻˇāĻžā§° āĻāĻŋāĻĒ
Minus sign → change signs; then combine like terms.
āĻŦāĻŋāĻ¯āĻŧā§āĻ āĻāĻŋāĻšā§āĻ¨ āĻĻā§āĻāĻŋāĻ˛ā§ → āĻāĻŋāĻšā§āĻ¨ āĻ¸āĻ˛āĻžāĻāĻ; āĻ¤āĻžā§° āĻĒāĻŋāĻāĻ¤ āĻāĻā§āĻ§ā§°āĻŖā§° āĻĒāĻĻ āĻ¯ā§āĻ āĻā§°āĻāĨ¤