Factorising the expression [tex]\(7x^2 y^3 - 14xy^2\)[/tex] involves breaking it down into simpler components that, when multiplied together, give you the original expression. Here's a step-by-step solution:
1. Identify the Greatest Common Factor (GCF):
First, we need to find the greatest common factor of the coefficients and the variables in each term of the expression.
- The coefficients are 7 and 14. The GCF of 7 and 14 is 7.
- The variable part involves [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. In [tex]\(7x^2 y^3\)[/tex], the minimum power of [tex]\(x\)[/tex] is 1 (appeared in [tex]\(14xy^2\)[/tex]) and the minimum power of [tex]\(y\)[/tex] is 2 (appeared in [tex]\(14xy^2\)[/tex]).
Therefore, the GCF for the entire expression is [tex]\(7xy^2\)[/tex].
2. Factor out the GCF:
We factor [tex]\(7xy^2\)[/tex] out of each term in the expression:
[tex]\[
7x^2 y^3 - 14xy^2 = 7xy^2 ( \frac{7x^2 y^3}{7xy^2} - \frac{14xy^2}{7xy^2})
\][/tex]
3. Simplify each term inside the parenthesis:
- For the first term: [tex]\( \frac{7x^2 y^3}{7xy^2} = x \cdot y = xy \)[/tex]
- For the second term: [tex]\( \frac{14xy^2}{7xy^2} = 2 \)[/tex]
Substituting these back in, we get:
[tex]\[
7x^2 y^3 - 14xy^2 = 7xy^2 (xy - 2)
\][/tex]
Thus, the factored form of the expression [tex]\(7x^2 y^3 - 14xy^2\)[/tex] is:
[tex]\[
7xy^2 (xy - 2)
\][/tex]
So, the final factorised expression is:
[tex]\[
7xy^2 (xy - 2)
\][/tex]
