Question

factorise 25a2-64b2​

Answer 1

Answer:

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

(25 • (a2)) - 26b2

STEP

2

:

Equation at the end of step

2

:

52a2 - 26b2

STEP

3

:

Trying to factor as a Difference of Squares

3.1 Factoring: 25a2-64b2

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 : 64 is the square of 8

Check : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (5a + 8b) • (5a - 8b)

Final result :

(5a + 8b) • (5a - 8b)

Step-by-step explanation:

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