Find factors of 3x2 - 75y2?
Answers
Answer:
3 • (x + 5y) • (x - 5y)
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Step-by-step explanation:
Step by Step Solution:
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Reformatting the input :
Changes made to your input should not affect the solution:
(1): "y2" was replaced by "y^2". 1 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
(3 • (x2)) - (3•52y2)
STEP
2
:
Equation at the end of step
2
:
3x2 - (3•52y2)
STEP
3
:
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
3x2 - 75y2 = 3 • (x2 - 25y2)
Trying to factor as a Difference of Squares:
4.2 Factoring: x2 - 25y2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 25 is the square of 5
Check : x2 is the square of x1
Check : y2 is the square of y1
Factorization is : (x + 5y) • (x - 5y)
Final result :
3 • (x + 5y) • (x - 5y)