Question

(x²y)²-4x²y²(factorise)​

Answer 1

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→ (x²y)² - 4x²y²

→ x⁴y² - 4x²y²

→ x²y² (x² - 4)

→ x²y² (x² - 2²)

→ x²y² (x + 2) (x - 2)

Answer 2

Given Expression :

• (x²y)²- 4x²y²

To Do :

• Factorise the given expression.

Step 1 :

Equation at the end of step 1 :

⟹ (((x²) • y)²) - (22x² • y²)

Pulling out like terms :

Pull out like factors :

⟹ x⁴y² - 4x²y² = x²y² • (x² - 4)

Trying to factor as a Difference of Squares:

Factoring : x² - 4

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 : x² is the square of x¹

∴ Factorization is : (x + 2) • (x - 2)

Final result :

∴ x²y² • (x + 2) • (x - 2)

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