In which square model will (9x^2+30x+25) appear?
Answer and explanation
Correct answer: square of side (3x+5)
The expression \(9x^2+30x+25\) has the pattern of a square identity. The first term is \(9x^2=(3x)^2\), and the last term is \(25=5^2\). For the square of a sum, the middle term must be twice the product of these two quantities: \(2\cdot3x\cdot5=30x\). This exactly matches the given middle term.
Therefore, the expression is \((3x+5)^2\), because expanding it gives \((3x+5)^2=9x^2+30x+25\). A side of \(9x+25\) would produce a different expansion, and \((3x-5)^2\) would have a negative middle term, namely \(-30x\). Hence the square model with side \(3x+5\), option A, is correct.
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What is the correct answer to this question?
square of side (3x+5)
Why is this the correct answer?
The expression \(9x^2+30x+25\) has the pattern of a square identity. The first term is \(9x^2=(3x)^2\), and the last term is \(25=5^2\). For the square of a sum, the middle term must be twice the product of these two quantities: \(2\cdot3x\cdot5=30x\). This exactly matches the given middle term.
Therefore, the expression is \((3x+5)^2\), because expanding it gives \((3x+5)^2=9x^2+30x+25\). A side of \(9x+25\) would produce a different expansion, and \((3x-5)^2\) would have a negative middle term, namely \(-30x\). Hence the square model with side \(3x+5\), option A, is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.
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