Step by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "b2" was replaced by "b^2". 1 more similar replacement(s).
Step 1 :
Equation at the end of step 1 :
(225 • (a2)) - (22•32b2)Step 2 :
Equation at the end of step 2 :
(32•52a2) - (22•32b2)
Step 3 :
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
225a2 - 36b2 = 9 • (25a2 - 4b2)
Trying to factor as a Difference of Squares :
4.2 Factoring: 25a2 - 4b2
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 : 4 is the square of 2
Check : a2 is the square of a1
Check : b2 is the square of b1
Factorization is : (5a + 2b) • (5a - 2b)
Final result :
9 • (5a + 2b) • (5a - 2b)
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