Question

We're trying to factorize
(125x3 + 512y;) using a suitable
algebraic identity.
This is what we get:
(5x + Py)(Qx2 + 64y2 + Rxy)
Find the missing values.

Answer 1

FactoringFactors of Algebraic expressions

In an algebraic expression, while factoring, terms are formed as products of factors. For example, in the algebraic expression 7xy+3, The term 7xy has been formed by the factors 7, x and y, i.e., 7xy = 7×x×y

Here we observe that the factors 7, x and y of 7xy cannot further be expressed as a product of factors. While factoring algebraic expressions the “prime” word is replaced by “irreducible”, therefore we may also say that 7, x and y are the prime factors or the irreducible forms of 7xy.

It should, however, be noted that 7×(xy) is not an irreducible form of 7xy since the factor xy can be further expressed as a product of x and y, i.e., xy = x×y. Let’s consider another expression 5x (x+4). It can be written as a product of factors. 5, x and (x+2). 5x(x+4) = 5×x×(x+4). The factors 5, x and (x+4) are irreducible factors of 5x (x+4).