Question

81 x power 4 - 121 x square​

Answer 1

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${81x^4}$ -$121x^2$.

=$(9x^2)^2$ -$(11x)^2$.

=$(9x^2-11x)$$(9x^2+11x)$

[using the formula a^2 - b^2 = (a+b)(a-b).

Answer 2

81x4-121x2

Final result :

x2 • (9x + 11) • (9x - 11)

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(81 • (x4)) - 112x2

Step 2 :

Equation at the end of step 2 :

34x4 - 112x2

Step 3 :

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

81x4 - 121x2 = x2 • (81x2 - 121)

Trying to factor as a Difference of Squares :

4.2 Factoring: 81x2 - 121

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 : 81 is the square of 9

Check : 121 is the square of 11

Check : x2 is the square of x1

Factorization is : (9x + 11) • (9x - 11)

Final result :

x2 • (9x + 11) • (9x - 11)

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