Which shows a perfect square trinomial?
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
16 x squared + 24 x y + 9 y squared if you meant
16x^2 + 24xy + 9y^2
What is the product?
negative 9 x (5 minus 2x)
18 x squared minus 45 x
negative 18 x squared minus 45 x
negative 18 x minus 45 x
18 x minus 45 x
A perfect square trinomial is a trinomial that can be factored into the square of a binomial. To determine which of the options is a perfect square trinomial, we need to check if it can be factored in the form (a + b)^2.
Let's go through each option:
1) 50y^2 - 4x^2
This is not a perfect square trinomial since it cannot be factored as (a + b)^2.
2) 100 - 36x^2y^2
This is not a perfect square trinomial since it cannot be factored as (a + b)^2.
3) 16x^2 + 24xy + 9y^2
This is a perfect square trinomial because it can be factored as (4x + 3y)^2.
4) 49x^2 - 70xy + 10y^2
This is not a perfect square trinomial since it cannot be factored as (a + b)^2.
So, the answer is 16x^2 + 24xy + 9y^2 is the perfect square trinomial.
A perfect square trinomial is a trinomial that can be factored into a square of a binomial. To determine which of the given expressions is a perfect square trinomial, we can factor each expression and see if it fits the form of a square of a binomial.
Let's factor each expression:
1) 50y^2 - 4x^2
This expression does not factor into a perfect square trinomial.
2) 100 - 36x^2y^2
This expression is in the form a^2 - b^2, which can be factored as (a + b)(a - b).
In this case, a = 10 and b = 6xy.
Therefore, the expression can be factored as (10 + 6xy)(10 - 6xy).
This is not a perfect square trinomial.
3) 16x^2 + 24xy + 9y^2
This expression is already in trinomial form.
To determine if it is a perfect square trinomial, we can use the formula (a + b)^2 = a^2 + 2ab + b^2.
Comparing this formula to the given expression, we see that a = 4x and b = 3y.
Plugging in these values, we get:
(4x + 3y)^2 = (4x)^2 + 2(4x)(3y) + (3y)^2 = 16x^2 + 24xy + 9y^2
Therefore, this expression is a perfect square trinomial.
4) 49x^2 - 70xy + 10y^2
This expression is not a perfect square trinomial.
So, out of the given expressions, the perfect square trinomial is:
16x^2 + 24xy + 9y^2