Question

Q1. Factorise completely
162 x⁵y- 82xy⁵​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

23t2 - 162

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

8t2 - 162 = 2 • (4t2 - 81)

Trying to factor as a Difference of Squares:

3.2 Factoring: 4t2 - 81

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 : 81 is the square of 9

Check : t2 is the square of t1

Factorization is : (2t + 9) • (2t - 9)

Final result :

2 • (2t + 9) • (2t - 9)