Factorise
X^2y + x^2 -4xy- 16
x^2y + x^2 -4xy- 16
= xy(x-4) + x^2-16
= xy(x-4) + (x+4)(x-4)
= (xy+x+4)(x-4)
To factorize the expression x^2y + x^2 - 4xy - 16, we can group the terms in pairs:
x^2y + x^2 - 4xy - 16
Group the first two terms and the last two terms:
(x^2y + x^2) - (4xy + 16)
Now, let's factor out the common terms from each group:
x^2(y + 1) - 4x(y + 4)
Simplify further:
x(x(y + 1) - 4(y + 4))
Now, let's distribute the x to each term inside the parentheses:
x(y^2 + y - 4y - 16)
Finally, combine like terms:
x(y^2 - 3y - 16)
So, the factored form of the expression x^2y + x^2 - 4xy - 16 is x(y^2 - 3y - 16).
To factorize the expression x^2y + x^2 - 4xy - 16, we can look for common factors among the terms.
Let's group the terms and factor them separately:
(x^2y + x^2) - (4xy + 16)
Now, let's factor out the common terms from each group:
x^2(y + 1) - 4x(y + 4)
Next, we can factor out the common factor, (y + 1):
(y + 1)(x^2 - 4x)
Finally, we can factor the quadratic expression, x^2 - 4x, by finding two numbers that multiply to -4 and add up to -4. The numbers are -2 and -2. So, we can rewrite the expression as:
(y + 1)(x - 2)(x - 2)
Therefore, the fully factorized expression is (y + 1)(x - 2)^2.