Choose the factorised form of (4x^2+12x+9).
Answer and explanation
Correct answer: ((2x+3)^2)
A quadratic is a perfect square when it follows the pattern \\(a^2+2ab+b^2=(a+b)^2\\). Here, the first term \\(4x^2\\) is the square of \\(2x\\), and the constant term 9 is the square of 3. The middle term must therefore be \\(2\cdot2x\cdot3=12x\\), which is exactly the middle term given.
Thus \\(4x^2+12x+9=(2x)^2+2(2x)(3)+3^2=(2x+3)^2\\). Option A is correct. The expression with a minus sign would produce a negative middle term, so option B cannot work. The square \\( (4x+9)^2\\) has an incorrect leading term and constant, and multiplying option D gives a different middle term and constant. Checking all three parts prevents a sign or square-root mistake.
Frequently asked questions
What is the correct answer to this question?
((2x+3)^2)
Why is this the correct answer?
A quadratic is a perfect square when it follows the pattern \\(a^2+2ab+b^2=(a+b)^2\\). Here, the first term \\(4x^2\\) is the square of \\(2x\\), and the constant term 9 is the square of 3. The middle term must therefore be \\(2\cdot2x\cdot3=12x\\), which is exactly the middle term given.
Thus \\(4x^2+12x+9=(2x)^2+2(2x)(3)+3^2=(2x+3)^2\\). Option A is correct. The expression with a minus sign would produce a negative middle term, so option B cannot work. The square \\( (4x+9)^2\\) has an incorrect leading term and constant, and multiplying option D gives a different middle term and constant. Checking all three parts prevents a sign or square-root mistake.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Factorisation.
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