Which of the following is the square of a binomial?[tex]A)c^2-2cd-d^2\\\\B)a^2+b^2\\\\C)4m^2-6mn+9n^2\\ \\D)16x^2+24xy+9y^2[/tex]
Accepted Solution
A:
ANSWERD. [tex]16 {x}^{2} + 24xy + 9 {y}^{2} [/tex]EXPLANATIONWe want to find the expression which is a square of a binomial.In other words, we want to identify the expression which is a perfect square trinomial.[tex]16 {x}^{2} + 24xy + 9 {y}^{2} [/tex]This expression can be rewritten as,[tex] {(4x)}^{2} + 2(4 \times 3)xy + {(3y)}^{2} [/tex]This is a perfect square trinomial that can be factored as:[tex] {(4x)}^{2} + 2(4 \times 3)xy + {(3y)}^{2} = (4x + 3y) ^{2} [/tex]This is the square of a binomial.The correct answer is D