Question

Simplify the following:

(a + 5b)² – (a – 5b)²

Answer 1

Step 1: Use the difference of squares identity

The expression follows the form of the difference of squares, X² – Y², which simplifies to (X – Y)(X + Y).

Here, we let X = a + 5b and Y = a – 5b.

Step 2: Substitute X and Y into the identity

Substitute the values into the factored form (X – Y)(X + Y):

((a + 5b) – (a – 5b))((a + 5b) + (a – 5b))

Step 3: Simplify the terms within the parentheses

Simplify the first parenthesis (X – Y):

(a + 5b – a + 5b) = 10b

Simplify the second parenthesis (X + Y):

(a + 5b + a – 5b) = 2a

Step 4: Multiply the simplified terms

Multiply the results from Step 3:

(10b)(2a) = 20ab