NCERT Solutions Class 8 Maths Chapter 6 — Algebraic Expressions & Identities

Solution:

Step 1: The terms in the expression 5xy - 3y + 7xz are 5xy, -3y, and 7xz. Ravi correctly identified these terms (ignoring the sign for 3y in his list, but implicitly including it in the original expression).

Step 2: The coefficient is the numerical factor of a term. For the term -3y, the numerical factor is -3, not 3. Ravi made an error in identifying the coefficient of y.

Solution:

Step 1: A monomial has one term. 4x - 5y + 3 has three terms, so it's a trinomial, not a monomial.

Step 2: A binomial has two terms. 7p²q has only one term, so it's a monomial, not a binomial.

Step 3: x² + y² has two terms (x² and y²), making it a binomial. This statement is TRUE.

Step 4: A polynomial cannot have terms with negative exponents or fractional exponents. These would make it not a polynomial.

Solution:

Step 1: The original expression is (7x - 4y) - (3x - 2y).

Step 2: When removing the parentheses from the second expression, the negative sign must be distributed to both terms inside: -(3x - 2y) becomes -3x + 2y.

Step 3: The student wrote 7x - 4y - 3x - 2y, which shows that they incorrectly changed -2y to -2y instead of +2y. This is an incorrect distribution of the negative sign.

Step 4: The correct simplification would be 7x - 4y - 3x + 2y = (7x - 3x) + (-4y + 2y) = 4x - 2y.

Solution:

Step 1: The Distributive Property states that a × (b + c) = (a × b) + (a × c).

Step 2: When multiplying a monomial (like 'a') by a polynomial (like 'b + c'), the monomial is distributed to each term of the polynomial.

Step 3: For example, 2x(3x + 5) = (2x × 3x) + (2x × 5) = 6x² + 10x. This demonstrates the distributive property.

Solution:

Step 1: When multiplying two binomials, (a + b) and (c + d), you take each term from the first binomial and multiply it by the entire second binomial.

Step 2: So, the term 'a' from the first binomial multiplies (c + d), giving a(c + d).

Step 3: And the term 'b' from the first binomial also multiplies (c + d), giving b(c + d).

Step 4: These two results are then added together: a(c + d) + b(c + d).