A gift box is a cuboid whose length, height and width are marked in the picture. Which monomial gives its volume?

Class 8Algebraic Expressions and IdentitiesAlgebra

Step-by-Step Solution

Volume

= 5 ab \times 3 a \times 2 b = (5 \times 3 \times 2) (a \times a) (b \times b) = 30 a^{2} b^{2}

. Multiply the numbers and add the powers of each letter.

Answer: D)

30 a^{2} b^{2}

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}

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