NCERT Solutions Class 8 Maths Chapter 13 — Factorization

Solution:

Step 1: Factorization is essentially the reverse process of multiplication.

Step 2: When we factorize an algebraic expression, we express it as a product of two or more simpler expressions, which are called its factors.

Solution:

Step 1: Identify the terms: 6xy and -9x.

Step 2: Find the GCF of the numerical coefficients (6 and 9) which is 3. Find the GCF of the variables (xy and x) which is x. So, the overall GCF is 3x.

Step 3: Divide each term by 3x: (6xy) ÷ (3x) = 2y and (-9x) ÷ (3x) = -3.

Step 4: Write the expression as the product of the GCF and the remaining terms: 3x(2y - 3).

Solution:

Step 1: Check Step 1: The GCF of 12 and 18 is 6. The GCF of a²b and ab² is ab. So, the GCF is 6ab. Step 1 is correct.

Step 2: Check Step 2: (12a²b) ÷ (6ab) = 2a, which is correct. (18ab²) ÷ (6ab) = 3b, which is also correct. Step 2 is correct.

Step 3: Check Step 3: Since the original expression had a '+' sign between the terms, the terms inside the bracket should also be added. 6ab(2a + 3b) is correct. Step 3 is correct.

Step 4: All steps in Rahul's solution are completely correct.

Solution:

Step 1: Group the terms in pairs that have a common factor: (ab + bc) + (ax + cx).

Step 2: Factor out the common factor from each group: b(a + c) + x(a + c).

Step 3: Now, (a + c) is a common binomial factor. Factor it out from the entire expression: (a + c)(b + x).

Solution:

Step 1: The given expression is 7p²q - 14pq².

Step 2: The greatest common factor (GCF) of 7p²q and 14pq² is 7pq.

Step 3: Priya's factorization: 7pq(p - 2q) is correct and complete because 7pq is the GCF, and the expression inside the bracket cannot be further factorized by common factors.

Step 4: Rohan's factorization: 7(p²q - 2pq²) is partially correct because 7 is a common factor, but it is not the *greatest* common factor. The expression inside the bracket (p²q - 2pq²) can still be factorized by taking out pq.

Step 5: Therefore, only Priya's factorization is correct and complete.