Maharashtra Board Class 7 Chapter 8 Set 35 Algebraic Expressions and Operations on them Solutions

Question 1. Multiply:
(i) 16xy x 18xy
(ii) 23xy² x 4yz²
(iii) (12a + 17b) × 4c
(iv) (4x + 5y) × (9x + 7y)
Answer:
(i) 16xy x 18xy = 16 × 18 × xy x xy = 288x²y²
(ii) 23xy² x 4yz² = 23 x 4 x xy² × yz² = 92xy³z²
(iii) (12a + 17b) × 4c = 12a × 4c + 17b × 4c = 48ac + 68bc
(iv) (4x + 5y) × (9x + 7y) = 4x × (9x + 7y) + 5y × (9x + 7y) = (4x x 9x) + (4x x 7y) + (5y x 9x) + (5y x 7y) = 36x² + 28xy + 45xy + 35y² = 36x² + 73xy + 35y²
In simple words: To multiply algebraic expressions, distribute each term from the first expression to every term in the second, then combine like terms. Remember to multiply coefficients and add exponents for the same variables.

🎯 Exam Tip: Pay close attention to the signs of terms and correctly combine like terms to avoid errors. Practice distributive property thoroughly.

Question 2. A rectangle is (8x + 5) cm long and (5x + 3) cm broad. Find its area.
Answer: Solution: Length of the rectangle = (8x + 5) cm
Breadth of the rectangle = (5x + 3) cm
∴ Area of the rectangle = length × breadth
= (8x + 5) × (5x + 3)
= 8x × (5x + 3) + 5 × (5x + 3)
= (8x × 5x) + (8x × 3) + (5 × 5x) + (5 × 3)
= 40x² + 24x + 25x + 15
= 40x² + 49x + 15
∴ The area of the rectangle is (40x² + 49x + 15) sq. cm.
In simple words: The area of a rectangle is found by multiplying its length and breadth. When these are algebraic expressions, use the distributive property to multiply them and then combine any similar terms.

🎯 Exam Tip: Clearly state the formula for the area of a rectangle and show each step of the multiplication using the distributive property. Ensure all like terms are correctly combined for the final answer.