25r^2 - 30r + 9 =?

Question

25r^2 - 30r + 9 equals

a. (5r - 3)^2
b. (3r - 5)^2
c. (25r + 9)^2
d. (25r - 9)^2

I thought I had to factor this, ya know find multiples of nine that also can add up to 30, do I have it switched?

Answer 1

Remember that (a+b)^2 = a^2 + 2ab + b^2 and (a-b)^2 = a^2 - 2ab + b^2. So if this is a perfect square, then a has to be 5r and b has to be 3. Since we have a negative term in the middle, this means the answer is (5r - 3)^2. Multiplying this out, you can verify that the middle term is -30r.

Answer 2

It is not multiples of 9 that add up to 30 to be solved. You must find two numbers that when multiplied together, then added, equals 30.

5*-3 = -15*2 = -30
25*9 = 225*2 = 450

So clearly (a) and (b) are your choices left, but when looking at them, 5r*5r = 25r^2 and 3r*2r = 9r^2, so the first choice must be correct. The answer is (a), (5r-3)^2.

Answer 3

First thing to do is to look at the signs of the equations and signs of the answers. If we look at the signs in the equation, we see that b = -30 and c = +9. That indicates that the solution is of the form (ar - d)^2. This eliminates answer c.

The first term of one of the answers squared must = 25r^2.
The only answer that fits this solution is a.

Answer 4

answer a)

25r^2 is (5r)^2 and 9 is 3^2

Answer 5

a is the right choice
25r^2-30r+9
=(5r)^2-2*5r*3+(3)^2
=(5r-3)^2

Answer 6

sol if this is what u mean

solve(25 r^2-30 r+9=r, r)

r=(sqrt(61)+31)/50=0.7762049935181

r=(31-sqrt(61))/50=0.4637950064819

Answer 7

a. (5r-3)^2

Answer 8

a