Maharashtra Board Class 7 Chapter 8 Set 33 Algebraic Expressions and Operations on them Solutions

Question 1. Add:
(i) 9p + 16q; 13p + 2q
(ii) 2a + 6b + 8c; 16a + 13c + 18b
(iii) 13x² – 12y²; 6x² – 8y²
(iv) 17a²b² + 16c; 28c – 28a²b²
(v) 3y² – 10y + 16; 2y – 7
(vi) – 3y² + 10y – 16; 7y² + 8
Answer:
Solution:
i. \( (9p + 16q) + (13p + 2q) \)
\( = (9p + 13p) + (16q + 2q) \)
\( = 22p + 18q \)
ii. \( (2a + 6b + 8c) + (16a + 13c + 18b) \)
\( = (2a + 16a) + (6b + 18b) + (8c + 13c) \)
\( = 18a + 24b + 21c \)
iii. \( (13x^2 - 12y^2) + (6x^2 - 8y^2) \)
\( = (13x^2 + 6x^2) + [(-12y^2) + (-8y^2)] \)
\( = 19x^2 + (-20y^2) \)
\( = 19x^2 - 20y^2 \)
iv. \( (17a^2b^2 + 16c) + (28c - 28a^2b^2) \)
\( = [17a^2b^2 + (-28a^2b^2)] + (16c + 28c) \)
\( = -11a^2b^2 + 44c \)
v. \( (3y^2 - 10y + 16) + (2y - 7) \)
\( = 3y^2 + (-10y + 2y) + (16 - 7) \)
\( = 3y^2 - 8y + 9 \)
vi. \( (-3y^2 + 10y - 16) + (7y^2 + 8) \)
\( = (-3y^2 + 7y^2) + (10y) + (-16 + 8) \)
\( = 4y^2 + 10y - 8 \)
In simple words: To add algebraic expressions, identify and group like terms, which are terms having the same variables raised to the same powers. Then, combine the coefficients of these like terms to simplify the expression.

🎯 Exam Tip: Accurately identifying like terms and carefully handling the signs of coefficients are crucial steps. Organize your work by vertically aligning like terms or using brackets to prevent errors. Ensure all powers of variables are correctly transferred.

Maharashtra Board Class 7 Maths Chapter 8 Algebraic Expressions and Operations on them Practice Set 33 Intext Questions and Activities

Question 1. Answer the following questions. (Textbook pg. no. 57)
1. 3x + 4y = How many?
2. 3 guavas + 4 mangoes = 7 guavas.
3. 7m - 2n = 5m.
Answer:
Solution:
1. 3x and 4y are unlike terms. Hence, they cannot be added, further to get a single term.
2. No. Guava and mango are different fruits. Hence, 3 guavas + 4 mangoes & 7 guavas.
3. No. 7m and 2n are unlike terms. Hence, 7m - 2n \( \neq \) 5m.
In simple words: Algebraic expressions can only be added or subtracted if they contain like terms, meaning terms with the same variables raised to the same powers. Unlike terms cannot be combined into a single term because they represent different quantities.

🎯 Exam Tip: Understanding the concept of 'like terms' is fundamental in algebra. Students should clearly state why terms cannot be combined if they are unlike. Use proper mathematical symbols for inequality and ensure explanations are clear and concise.