Question

# Factor: x^{2}-8xy+12y^{2}

Polynomial factorization
Factor: $$x^{2}-8xy+12y^{2}$$

2021-05-22
Step 1
Factorization is the process of writing the polynomial as the product of its factors.
To factorize, first split the middle term such that the product of the split terms is equal to the product of the first term and the last term. So, split −8xy as −6xy−2xy because the product of the split terms is equal to $$x^{2}\times 12y^{2}$$.
$$x^{2}-8xy+12y^{2}=x^{2}-6xy-2xy+12y^{2}$$
Step 2
Now, factor out x and −2y from the first two terms and the last two terms respectively. Finally, factor out (x−6y).
$$x^{2}-6xy-2xy+12y^{2}=x(x-6y)-2y(x-6y)$$
=(x-6y)(x-2y)
Therefore, factor of $$x^{2}-8xy+12y^{2}$$ is (x-6y)(x-2y).