The product of (x + 5) and (x – 5) is ____________

Fill in the Blanks

The product of (x + 5) and (x – 5) is x² – 25

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Chapter 3: Algebra - Exercise 3.1 [Page 61]

Chapter 3 Algebra
Exercise 3.1 | Q 1. (ii) | Page 61

The value of p for 51² – 49² = 100p is 2.

Using suitable identities, evaluate the following.

(132)² – (68)²

Factorise the following using the identity a² – b² = (a + b)(a – b).

x² – 9

Factorise the following using the identity a² – b² = (a + b)(a – b).

4x² – 25y²

Factorise the following using the identity a² – b² = (a + b)(a – b).

`x^2/25 - 625`

The sum of first n natural numbers is given by the expression `n^2/2 + n/2`. Factorise this expression.

The sum of (x + 5) observations is x⁴ – 625. Find the mean of the observations.

The radius of a circle is 7ab – 7bc – 14ac. Find the circumference of the circle. `(pi = 22/7)`

Verify the following:

(p – q)(p² + pq + q²) = p³ – q³

Find the value of a, if pq²a = (4pq + 3q)² – (4pq – 3q)²