4a^2 − b^2 − 2a + b Simplify

Question

asked Apr 28, 2022 229k views

2 Answers

NIA · Answer 1 · 2022-05-04T13:32:15+0000

4a2-b2

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 : a2 is the square of a1

Check : b2 is the square of b1

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

Final result :

(2a + b) • (2a - b)