Question

when we factorise 36x^2y^2-1​

Answer 1

Answer:

2.1 Factoring: 36x2y2-1

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 : 1 is the square of 1

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (6xy + 1) • (6xy - 1)

Answer 2

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 : 1 is the square of 1

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (6xy + 1) • (6xy - 1)

Final result :

(6xy + 1) • (6xy - 1)