factorise 25÷16a^2-ab+4÷25b^2
Answers
Answer:
Answer stwp by step below
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
(16 • (a2)) - 52b2
STEP
2
:
Equation at the end of step
2
:
24a2 - 52b2
STEP
3
:
Trying to factor as a Difference of Squares
3.1 Factoring: 16a2-25b2
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 : 16 is the square of 4
Check : 25 is the square of 5
Check : a2 is the square of a1
Check : b2 is the square of b1
Factorization is : (4a + 5b) • (4a - 5b)
Final result :
(4a + 5b) • (4a - 5b)
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