Question

Factorise 4x2

-12x+9.​

Answer 1

Step-by-step explanation:

Factoring: 4x2-9

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 : x2 is the square of x1

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

Final result :

(2x + 3) • (2x - 3)

Answer 2

$4 {x}^{2} - 12x + 9 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = 4 {x}^{2} - 6x - 6x + 9 \: \: \: \: \: \: \: \: \: \: \\ = 2x(2x - 3) - 3(2x - 3) \\ = (2x - 3)(2x - 3) \: \: \: \: \: \: \: \: \: \: \: \: \\ = {(2x - 3)}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$