Question

1. Using suitable identity, factorize (4x² - 9).

2. Evaluate (249 × 250).
3. Factorize (2⁴ - 2⁴).
4. Factorize ((x + 1)² - (y - 1)²).
(A) (i) Difference of squares (ii) 62100 (iii) 0 (iv) (2x)
(B) (i) Perfect squares (ii) 62000 (iii) 16 (iv) (x + y)
(C) (i) Difference of squares (ii) 62250 (iii) 24 (iv) (x - y)
(D) (i) Perfect squares (ii) 62050 (iii) 32 (iv) (xy)

Answer 1

The expression (4x² - 9) is factorized using the difference of squares identity, yielding (2x - 3)(2x + 3). The product of 249 and 250 is evaluated to be 62,250, and the expression (2⁴ - 2⁴) is 0. Lastly, ((x + 1)² - (y - 1)²) is factorized into (x - y + 2)(x + y).

Step-by-step explanation:

Factorization and Evaluation of Expressions

Let's address each part of the student's question step by step:

1. Using suitable identity, factorize (4x² - 9). The expression is in the form of a² - b² which is a difference of squares. It can be factorized as (2x - 3)(2x + 3).
2. To evaluate (249 × 250), we can apply the multiplication. The result is 62,250.
3. Factorize (2⁴ - 2⁴). This expression is zero since anything minus itself is zero. There are no factors to be extracted from 0.
4. Factorize ((x + 1)² - (y - 1)²). This is also a difference of squares and can be factorized as ((x + 1) - (y - 1))((x + 1) + (y - 1)) which simplifies to (x - y + 2)(x + y).

Based on the identities used and calculations performed, the correct answers are: (i) Difference of squares (ii) 62,250 (iii) 0 (iv) (x - y + 2)(x + y). Therefore, the best matching option given to the student would be (A).