Question

factorise 20a2 -45b2​

Answer 1

Answer:

Changes made to your input should not affect the solution:

(1): "a2" was replaced by "a^2".

STEP

1

:

Equation at the end of step 1

(22•5a2) - 45

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

20a2 - 45 = 5 • (4a2 - 9)

Trying to factor as a Difference of Squares:

3.2 Factoring: 4a2 - 9

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 : 4 is the square of 2

Check : 9 is the square of 3

Check : a2 is the square of a1

Factorization is : (2a + 3) • (2a - 3)

Final result :

5 • (2a + 3) • (2a - 3)