Question

Expand the given term:
(x + 5)(x – 5)

Answer 1

Hint: To expand the given term we use basic multiplication and write it as a single term with an addition or a subtraction operation.

Completes step-by-step solution -
Given data,
(x + 5)(x – 5)

Now (x + 5) (x – 5) is in the form of (a – b) (a + b).

We also know the formula (a – b) (a + b) = ${{\text{a}}^2} - {{\text{b}}^2}$

Comparing with the above equation we get a = x and b = 5.

Therefore, (x + 5) (x – 5) = ${{\text{x}}^2}{\text{ - }}{{\text{5}}^2}$

Note: The key in solving such type of problems is to know the formula of (a – b) (a + b) =${{\text{a}}^2} - {{\text{b}}^2}$. We can also go about the problem using the normal multiplication method, which gives us the same answer.
⟹(x + 5) (x – 5) = ${{\text{x}}^2} + 5{\text{x - 5x - 25}}$
                       = ${{\text{x}}^2}{\text{ - 25}}$
                       = ${{\text{x}}^2}{\text{ - }}{{\text{5}}^2}$