The rectangle has width $3 p$ and length $2 p + 5$ , split into two parts as shown. Which expression gives its area?

Class 8Algebraic Expressions and IdentitiesAlgebra

Step-by-Step Solution

Area

= 3 p (2 p + 5) = 3 p \times 2 p + 3 p \times 5 = 6 p^{2} + 15 p

. Both parts must be multiplied by

3 p

Answer: A)

6 p^{2} + 15 p

Use the distributive property — multiply the monomial by EVERY term in the polynomial.

Example:

3 x \times (4 x^{2} - 5 x + 2) = 12 x^{3} - 15 x^{2} + 6 x

.

When multiplying powers of the same variable: **add the exponents**.

x^{2} \times x^{3} = x^{5}

Don't just memorise the answer — build a daily practice habit.