What is the simplified form of ( (5m-2n)^2-(5m+2n)^2 )?
Answer and explanation
Correct answer: (-40mn)
Use the identity \\( (u-v)^2-(u+v)^2=-4uv\\). Here, u=5m and v=2n. The first square has the minus form and the second square has the plus form, so their difference is negative. Substituting gives \\(-4(5m)(2n)=-40mn\\). Therefore option B is correct. The order of subtraction matters; changing it would change the sign of the result.
This can also be checked by expansion. The first square is \\(25m^2-20mn+4n^2\\), and the second is \\(25m^2+20mn+4n^2\\). Subtracting the second from the first cancels the two square terms and gives \\(-20mn-20mn=-40mn\\). Thus neither 40mn nor 20mn has the correct sign or magnitude. The expressions 25m² and 4n² are only parts of the expansion, not the final simplified difference.
Frequently asked questions
What is the correct answer to this question?
(-40mn)
Why is this the correct answer?
Use the identity \\( (u-v)^2-(u+v)^2=-4uv\\). Here, u=5m and v=2n. The first square has the minus form and the second square has the plus form, so their difference is negative. Substituting gives \\(-4(5m)(2n)=-40mn\\). Therefore option B is correct. The order of subtraction matters; changing it would change the sign of the result.
This can also be checked by expansion. The first square is \\(25m^2-20mn+4n^2\\), and the second is \\(25m^2+20mn+4n^2\\). Subtracting the second from the first cancels the two square terms and gives \\(-20mn-20mn=-40mn\\). Thus neither 40mn nor 20mn has the correct sign or magnitude. The expressions 25m² and 4n² are only parts of the expansion, not the final simplified difference.
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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