Question & Answer
QUESTION

Factories the following expressions:
${\text{a}}{{\text{x}}^{\text{2}}}{\text{y + bx}}{{\text{y}}^{\text{2}}}{\text{ + cxyz}}$
A. xy(ax+by+cz)
B. axy(x+by+cz)
C. bxy(ax+y+cz)
D. xy(ax+by+cz)

ANSWER Verified Verified
Hint: Factorization (also called factorization and factoring) is taking a composite number apart into numbers that multiply together to get the original number. These smaller numbers are called factors or divisors. For example, 12 can be factored as 4 × 3. So, here we will take out the common factors.

Complete step-by-step answer:
We have,
${\text{a}}{{\text{x}}^{\text{2}}}{\text{y + bx}}{{\text{y}}^{\text{2}}}{\text{ + cxyz}}$
In this expression we have three terms, and also
We observe, common factor in all these terms is xy.
So, we take common & we get,
xy(ax+by+cz).
Therefore, option (D) is correct.

Note: In elementary algebra, factoring a polynomial reduces the problem of finding its roots to finding the roots of the factors. Factorization may also refer to more general decompositions of a mathematical object into the product of smaller or simpler objects.
And also Factoring is a useful skill in real life. Common applications include: dividing something into equal pieces, exchanging money, comparing prices, understanding time and making calculations during travel.