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Lesson eLearning

Expand the product $(3 m - 2 n) (4 m + 5 n)$ .

medium 2 marks Class 7 · Mathematics · Algebraic Expressions

Answer

12m^2 + 7mn - 10n^2

The correct answer is 12m^2 + 7mn - 10n^2 — Write the expanded expression: $12 m^{2} + 7 mn - 10 n^{2}$ .

Step-by-step solution

Apply the distributive property: $(3 m) (4 m)$ .
Compute $3 m \times 4 m = 12 m^{2}$ .
Apply the distributive property: $(3 m) (5 n)$ .
Compute $3 m \times 5 n = 15 mn$ .
Apply the distributive property: $(- 2 n) (4 m)$ .
Compute $- 2 n \times 4 m = - 8 mn$ .
Apply the distributive property: $(- 2 n) (5 n)$ .
Compute $- 2 n \times 5 n = - 10 n^{2}$ .
Combine like terms $15 mn$ and $- 8 mn$ to get $7 mn$ .
Write the expanded expression: $12 m^{2} + 7 mn - 10 n^{2}$ .

Common mistake: Missing one of the product terms

Concept tested: Distributive property (expansion)

Published 4 October 2026 · How this solution was prepared and checked

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