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Mathematical textbooks state that a perfect square trinomial is defined as expressions that can be factored into the square of a binomial, hence verifying that only 16x2+24xy+9y2 fits this definition. Now, let's check each option to see if it matches this pattern: The middle term does not meet the criteria for a perfect square trinomial
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The expression $$16x^ {2} + 24xy + 9y^ {2}$$16x2 +24xy +9y2 represents a perfect square trinomial. When expanded, it takes the form The perfect square trinomial is
16x² + 24xy + 9y²
This is not even a trinomial, rather a binomial expression • 3rd expression = 16x² + 24xy + 9y² = (4x)² + (2 * 4x + 3y) + (3y)² This solution was automatically generated by our smart calculator
4 x 2 1 2 x + 9 4x2 −12x+9 The trinomial 4 x 2 1 2 x + 9 4x2 −12x+9 is a perfect square trinomial, because it's discriminant is equal to zero. The expression that shows a perfect square trinomial is c 16x2 + 24xy + 9y2, which can be factored as (4x +3y)2
The other options do not meet the criteria for a perfect square trinomial.
Thus, the expression that represents a perfect square trinomial is clearly option c Algebraic principles confirm that perfect square trinomials can be derived from the expansion of binomials, following the identity (a+b)2=a2+2ab+b2 16x^2 + 24xy + 9y^2 is a perfect square trinomial The correct option is (c).
To identify a perfect square trinomial, we look for a trinomial that can be expressed in the form (ax + by)2 = a2x2 + 2abxy + b2y2 This means that the first term is a perfect square, the last term is also a perfect square, and the middle term is twice the product of the two square roots. Kylie did not understand that this is a perfect square trinomial, and she did not determine the product correctly The product shown is a difference of squares
What is the missing constant term in the second factor?
50 y squared minus 4 x squared 100 minus 36 x squared y squared 16 x squared + 24 x y + 9 y squared 49 x squared minus 70 x y + 10 y squared asked by guest on sep 25, 2025 at 7:41 am mathbot answer: To determine which expression is a perfect square trinomial, we need to understand the form of a perfect square trinomial A perfect square trinomial can be expressed as (ax + by)2
