Question

Factor the expression below.

25x2 + 30x + 9
(5x - 3)(5x-3)
B. (25x+3)(x+3)
C. (5x+3)(5x + 3)
D. (25x - 3)(x-3).

Answer 1

I'm glad you asked!

Explanation:

Factor
`25x2+30x+9`

`25x2+30x+9`

`=(5x+3)(5x+3)`

Answer:

`=(5x+3)(5x+3)`

Answer 2

Answer: C. (5x+3)(5x+3)

Explanation:

This is assuming this is a quadratic with 25x2 actually being 25x^2

We can start by simplifying the 25 to be 5^2

As well as the 9 to be 3^2

The expression now looks like:
`5^(2)x^(2) + 30x + 3^2`

Now we can apply an exponent rule to the 5^2 x^2

The rule states:
`a^(m)b^(m) = (ab)^m`

So this means:
`5^(2)x^(2) = (5x)^2`

We can now rewrite 30x as 2 * 5x * 3

The expression now looks like:
`(5x)^(2) + 2 * 5x * 3 + 3^(2)`

Now this expression matches with the perfect square formula which states:

`(a+b)^(2) = a^(2) +2* a * b + b^(2)`

Our a value is 5x and our b value is 3.

So:
`(a+b)^(2) = (5x+3)^(2)`

The answer is (5x+3)(5x+3)