factoring completely:
36x^2 + 60x +25
36x^2 + 60x +25
=(6x)^2+2*5*(6x)+5^2
Does that look familiar?
To factor the quadratic expression completely, you can look for two binomial factors that multiply together to give you the original expression.
Given the expression: 36x^2 + 60x + 25
Step 1: Check if the quadratic expression can be factored using the perfect square trinomial form: a^2 + 2ab + b^2 = (a + b)^2.
In this case, a = 6x and b = 5.
Step 2: Square the value of a, which is 6x, and square the value of b, which is 5.
(6x)^2 = 36x^2
(5)^2 = 25
Step 3: Compare the resulting expression from step 2, which is 36x^2 + 25, with the original expression: 36x^2 + 60x + 25
If the resulting expression matches the original expression, then the quadratic expression can be factored.
Step 4: Replace the middle term of the original expression, 60x, with the two corresponding terms from step 3, which are 2ab: (2 * 6x * 5).
36x^2 + 60x + 25 = 36x^2 + 2(6x)(5) + 25
Step 5: Factor by grouping. Group the first two terms and the last two terms separately.
36x^2 + 2(6x)(5) + 25 = (36x^2 + 2(6x)(5)) + 25
Step 6: Factor out the greatest common factor from each group.
36x^2 + 2(6x)(5) = 2(6x)(6x + 5) = 12x(6x + 5)
Step 7: Combine the factored groups.
12x(6x + 5) + 25 = 12x(6x + 5) + 25
So, the completely factored form of the quadratic expression 36x^2 + 60x + 25 is 12x(6x + 5) + 25.