SOLUTION: Factor the following into the product of two binomials. Then, confirm your answer is correct by multiplying the two binomials: 25y2 + 20y + 4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor the following into the product of two binomials. Then, confirm your answer is correct by multiplying the two binomials: 25y2 + 20y + 4       Log On


   

Question 105095: Factor the following into the product of two binomials. Then, confirm your answer is correct by multiplying the two binomials:
25y2 + 20y + 4

Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
25y2+%2B+20y+%2B+4
To factor this, please rad my lesson first! It is entitled:Factoring trinomials: SHORTCUT!!!Factoring trinomials: SHORTCUT!!!
Then, go back to this page.
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By the use of the quadratic formula,
y=%28-20%2B-sqrt%2820%5E2-4%2A25%2A4%29%29%2F%282%2A25%29
y=%28-20%2B-sqrt%28400-400%29%29%2F%2850%29
y=%28-20%2B-+0%29%2F%2850%29
y=-20%2F50
y=-2%2F5
If y=-2%2F5,
5y%2B2=0
Since one solution is obtained, this polynomial is a perfect square trinomial and thus,
25y2+%2B+20y+%2B+4=%285y%2B2%29%5E2

CHECK:
%285y%2B2%29%5E2=%285y%2B2%29%285y%2B2%29
%285y%2B2%29%5E2=5y%285y%2B2%29%2B2%285y%2B2%29
%285y%2B2%29%5E2=%2825y%5E2%2B10y%29%2B%2810y%2B4%29
%285y%2B2%29%5E2=25y%5E2%2B%2810y%2B10y%29%2B4
%285y%2B2%29%5E2=25y%5E2%2B20y%2B4
Therefore, the solution is correct and my lesson is reliable!

Power up,
HyperBrain!