Factorise
4x² + 9y² + 16z² + 12xy - 24yz - 16xy
Answers
Correct Question:
- Factorise 4x² + 9y² + 16z² + 12xy - 24yz - 16xz
Solution:
We have to factorise the given expression.
= 4x² + 9y² + 16z² + 12xy - 24yz - 16xz
It can be written as:
= 4x² + 9y² + 16z² + 2[6xy - 12yz - 8xz]
= (2x)² + (3y)² + (4z)² + 2[6xy - 12yz - 8xz]
We can observe that it is in the form a² + b² + c² + 2(ab + bc + ac) which can be factored into (a + b + c)²
But, two of its terms are negative. Let us determine among (2x), (3y) and (4z) which term is negative.
-12yz is negative means anyone of (3y) and (4z) is negative.
If 4z is negative, then 2x must be positive so that their product is negative.
So, if 4z is negative 3y must be positive such that their product is negative.
Therefore:
→ 2x is positive.
→ 3y is positive.
→ 4z is negative.
So, the expression can be written as:
= (2x)² + (3y)² + (-4z)² + 2 × [(2x) × (3y) + (3y) × (-4z) + (-4z) × (2x)]
= (2x + 3y - 4z)²
★ Which is our required answer.
Answer:
- Factorisation of the expression is (2x + 3y - 4z)²