Question

Factorise:y2 - xy(1- x) - x3
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Answer 1

Given -

• y² - xy(1 - x) - x³

Solution -

→ y² - xy(1 - x) - x³

→ y² - xy + x²y - x³

• Rearranging

→ - xy + y² - x³ + x²y

• Take common

→ -y(x + y) - x²(x + y)

→ (x + y)(x² - y)

(x + y)(x² - y) are the factors of y² - xy(1 - x) - x³

Focus Zone -

★ (a + b)³ = a³ + b³ + 3ab(a + b)

★ (a - b)³ = a³ - b³ - 3ab(a - b)

★ a³ - b³ = (a - b)(a² + ab + b²)

★ a³ + b³ = (a + b)(a² - ab + b²)

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Answer 2

Answer:

Given :-

• y² - xy(1 - x) - x³

To Find :-

• What is the factories of that above equation.

Solution :-

y² - xy(1 - x) - x³

⇒ y² - xy - x²y - x³

By taking out common in all terms we get,

⇒ y(y - x) + x²(y - x)

➠ (y - x)(y + x²)

∴ The factorization of y² - xy(1 - x) - x³ is (y - x)(y + x²).