Question

Factroize the following expressions:1. a²- 4

Answer 1

Answer:

$a {}^{2} - 4 \\ a { }^{2} - 2 { }^{2} ((a {}^{2} - b {}^{2} ) = (a - b)(a + b) \\ ( a - 2)(a + 2) \\ factor \: of \: a { }^{2} - 4 \: is \: (a - 2)(a + 2)$

refer the given answer

Answer 2

Answer:

a2-4

Final result :

(a + 2) • (a - 2)

Step by step solution :

Step 1 :

Trying to factor as a Difference of Squares :

1.1 Factoring: a2-4

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

Factorization is : (a + 2) • (a - 2)

Final result :

(a + 2) • (a - 2)