Question

Find the factors of 25a2-4b2​

Answer 1

Answer:

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 :

(5a + 2b) • (5a - 2b)