Question

Identify each expression that can be factored using the perfect square trinomial pattern.

1. n^2+10n+25
2. 4d^2+50d+100
3. 9x^2−24x+16
4. m^2+10m+16

Answer 1

Expressions 1 (n^2+10n+25) and 3 (9x^2−24x+16) can be factored using the perfect square trinomial pattern. Expressions 2 (4d^2+50d+100) and 4 (m^2+10m+16) do not fit the pattern and cannot be factored as such.

Step-by-step explanation:

The question is asking to identify which of the given expressions can be factored using the perfect square trinomial pattern. A perfect square trinomial pattern is a type of quadratic expression that can be written as the square of a binomial. We can recognize this pattern when the first and last terms are perfect squares, and the middle term is twice the product of the square roots of the first and last terms.

1. The expression n^2+10n+25 follows this pattern because 10n is twice the product of the square roots of n^2 and 25, which are n and 5 respectively.
2. The expression 4d^2+50d+100 does not follow this pattern because 50d is not twice the product of the square roots of 4d^2 (which is 2d) and 100 (which is 10).
3. The expression 9x^2-24x+16 does follow the pattern because -24x is twice the product of the square roots of 9x^2 (which is 3x) and 16 (which is 4).
4. The expression m^2+10m+16 does not follow this pattern because the middle term 10m does not equal twice the product of the square roots of m^2 and 16.

In conclusion, expressions 1 and 3 can be factored using the perfect square trinomial pattern, while expressions 2 and 4 cannot.