What is the value of ( (4m-3n)^2-(16m^2+9n^2) )?
Answer and explanation
Correct answer: -24mn
Use the identity
\((a-b)^2=a^2-2ab+b^2\). Thus,
\((4m-3n)^2=16m^2-24mn+9n^2\). Subtracting
\((16m^2+9n^2)\) cancels the square terms, leaving
\(-24mn\).
\(24mn\) has the wrong sign because the middle term in a square of a difference is negative. Exam tip: in
\((a-b)^2\), the middle term is always
\(-2ab\).
Frequently asked questions
What is the correct answer to this question?
-24mn
Why is this the correct answer?
Use the identity
\((a-b)^2=a^2-2ab+b^2\). Thus,
\((4m-3n)^2=16m^2-24mn+9n^2\). Subtracting
\((16m^2+9n^2)\) cancels the square terms, leaving
\(-24mn\).
\(24mn\) has the wrong sign because the middle term in a square of a difference is negative. Exam tip: in
\((a-b)^2\), the middle term is always
\(-2ab\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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