What is the simplified form of ((x+2y+z)^2-(x^2+4y^2+z^2))?
Answer and explanation
Correct answer: 4xy+2xz+4yz
The correct answer is A. Treat x, 2y, and z as the three terms in the square. Using (p+q+r)^2=p^2+q^2+r^2+2pq+2pr+2qr, we obtain (x+2y+z)^2=x^2+4y^2+z^2+4xy+2xz+4yz. The expression subtracts x^2+4y^2+z^2, so those three square terms cancel and only the pair-product terms remain: 4xy+2xz+4yz. Option B uses coefficients that are too small, as if the factor 2 had not been applied correctly to every pair. Options C and D assign the coefficients to the wrong pairs. The governing concept is the square of a sum of three terms and cancellation of like terms.
Frequently asked questions
What is the correct answer to this question?
4xy+2xz+4yz
Why is this the correct answer?
The correct answer is A. Treat x, 2y, and z as the three terms in the square. Using (p+q+r)^2=p^2+q^2+r^2+2pq+2pr+2qr, we obtain (x+2y+z)^2=x^2+4y^2+z^2+4xy+2xz+4yz. The expression subtracts x^2+4y^2+z^2, so those three square terms cancel and only the pair-product terms remain: 4xy+2xz+4yz. Option B uses coefficients that are too small, as if the factor 2 had not been applied correctly to every pair. Options C and D assign the coefficients to the wrong pairs. The governing concept is the square of a sum of three terms and cancellation of like terms.
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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