Question

factorize using suitable identity 36x2—25y2​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

(36 • (x2)) - 52y2

STEP

2

:

Equation at the end of step

2

:

(22•32x2) - 52y2

STEP

3

:

Trying to factor as a Difference of Squares:

3.1 Factoring: 36x2-25y2

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 : 36 is the square of 6

Check : 25 is the square of 5

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (6x + 5y) • (6x - 5y)

Final result :

(6x + 5y) • (6x - 5y)