Question

factozisation of x²-xy(1+y)+y³​

Answer 1

Correct question :

factozisation of x²+ xy ( 1 + y ) + y³

Answer :

⇛$(\:x\:+\:y\:)\:(\:x\:+\:y^2\:)$

Explanation :

⇛$x^2\:+\:xy\:(\:1\:+\:y\:)\:+\:y^3$

It can be written as,

⇛$x^2\:+\:xy\:+\:xy\:+\:y^3$

Take out common,

⇛$x(\:x\:+\:y\:)\:y^2\:(\:x\:+\:y\:)$

⇛$(\:x\:+\:y\:)\:(\:x\:+\:y^2\:)$

Definition of Factorisation :

Factorization consist of writing a number or another mathematical object as a product of several factors.

So, It's Done !!

Answer 2

Given :

• x² - xy(1 + y) + y³

To Find :

• Factorize the expression.

Required Solution :

⇛ x² - xy(1 + y) + y³

Apply the distributive property,

⇛ x² - xy × 1 - xy + y³

Multiply -1 by 1,

⇛ x² - xy - xy × y + y³

Move y,

⇛ x² - xy - x(y × y) + y³

Multiply y by y,

⇛ x² - xy - xy² + y³

Group the first two terms and the last two term,

⇛ (x² - xy) - xy² + y³

Factor out the greatest common factor (GCF) from each group,

⇛ x(x - 1y) - y² (x - y)

Factor the polynomial by factoring out the greatest common factor x - 1y,

⇛ (x -1y) (x - y²)

Rewrite -1y as -y

⇛ (x - 1) (x - y²)

Hence Solved !

$\:$

Additional Information :

✒ Factozisation :

Factorizing is to make a single term: try to write everything as products (multiplication), for example:

→ 6x² - 9x + 10 = (2x - 5) (3x - 2)

Step ① :

Find a common factor

Example:

→ 4xy + x⁴ + x = x(4x + x³ + 1)

Step ② :

Count the number of terms

(terms are separated by + or −)

If none of these methods work, re-arrange the terms, or remove brackets and start again.