Question

Express 9x^2 +16y^2 -24xy as a square of a binomial​

Answer 1

STEP
1
:
Equation at the end of step 1

(9 • (x2)) - 24y2
STEP
2
:

Equation at the end of step
2
:

32x2 - 24y2
STEP
3
:

Trying to factor as a Difference of Squares:

3.1 Factoring: 9x2-16y2

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 : 9 is the square of 3
Check : 16 is the square of 4
Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (3x + 4y) • (3x - 4y)

Final result :
(3x + 4y) • (3x - 4y)