Maharashtra Board Class 7 Chapter 8 Set 34 Algebraic Expressions and Operations on them Solutions

Question 1. Subtract the second expression from the first.
(i) (4xy - 9z); (3xy - 16z)
(ii) (5x + 4y + 7z); (x + 2y + 3z)
(iii) (14x² + 8xy + 3y²); (26x² - 8xy - 17y²)
(iv) (6x² + 7xy + 16y²); (16x² - 17xy)
(v) (4x + 16z); (19y - 14z + 16x)
Answer:
i. (4xy - 9z) - (3xy - 16z) = 4xy - 9z - 3xy + 16z = (4xy - 3xy) + (16z - 9z) = xy + 7z
ii. (5x + 4y + 7z) - (x + 2y + 3z) = 5x + 4y + 7z - x - 2y - 3z = (5x - x) + (4y - 2y) + (7z - 3z) = 4x + 2y + 4z
iii. (14x² + 8xy + 3y²) - (26x² - 8xy - 17y²) = 14x² + 8xy + 3y² - 26x² + 8xy + 17y² = (14x² - 26x²) + (8xy + 8xy) + (3y² + 17y²) = -12x² + 16xy + 20y²
iv. (6x² + 7xy + 16y²) - (16x² - 17xy) = 6x² + 7xy + 16y² - 16x² + 17xy = (6x² - 16x²) + (7xy + 17xy) + 16y² = -10x² + 24xy + 16y²
v. (4x + 16z) - (19y- 14z + 16x) = 4x + 16z - 19y + 14z - 16x = (4x - 16x) - 19y + (16z + 14z) = -12x - 19y + 30z
In simple words: To subtract algebraic expressions, change the sign of each term in the second expression and then combine like terms. This process simplifies the expression by grouping terms with the same variables and powers.

🎯 Exam Tip: Pay close attention to the signs when distributing the negative sign, as a common mistake is incorrect sign changes. Organize like terms vertically or horizontally for clarity and accuracy in combining them.