( x^2+12x+36 ) is the square of what?
Answer and explanation
Correct answer: ( (x+6)^2 )
A trinomial is a perfect square when it follows the pattern \\(x^2+2xy+y^2=(x+y)^2\\). The first term, \\(x^2\\), shows that one part of the bracket is \\(x\\). The last term, \\(36\\), is \\(6^2\\), so the other part is 6. The middle term must then be twice their product. Since \\(2\times x\times6=12x\\), the given expression matches the plus form.
Thus, \\(x^2+12x+36=x^2+2(x)(6)+6^2=(x+6)^2\\). Therefore option C is correct. The choices with 12 use the last number itself instead of its square root. The expression \\((x-6)^2\\) would produce \\(x^2-12x+36\\), so it cannot be correct because the middle term here is positive.
Frequently asked questions
What is the correct answer to this question?
( (x+6)^2 )
Why is this the correct answer?
A trinomial is a perfect square when it follows the pattern \\(x^2+2xy+y^2=(x+y)^2\\). The first term, \\(x^2\\), shows that one part of the bracket is \\(x\\). The last term, \\(36\\), is \\(6^2\\), so the other part is 6. The middle term must then be twice their product. Since \\(2\times x\times6=12x\\), the given expression matches the plus form.
Thus, \\(x^2+12x+36=x^2+2(x)(6)+6^2=(x+6)^2\\). Therefore option C is correct. The choices with 12 use the last number itself instead of its square root. The expression \\((x-6)^2\\) would produce \\(x^2-12x+36\\), so it cannot be correct because the middle term here is positive.
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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