Answer :
To factor the algebraic expression [tex]\(40x^4y^3 - 25x^3y\)[/tex], follow these steps:
1. Identify the Greatest Common Factor (GCF):
Look for common factors in the coefficients and the variables from both terms.
- Coefficients: The numbers are 40 and 25. The GCF of 40 and 25 is 5.
- Variables:
- For [tex]\(x^4\)[/tex] and [tex]\(x^3\)[/tex], the common factor is [tex]\(x^3\)[/tex].
- For [tex]\(y^3\)[/tex] and [tex]\(y\)[/tex], the common factor is [tex]\(y\)[/tex].
Combine these to find the overall GCF: [tex]\(5x^3y\)[/tex].
2. Factor Out the GCF:
Divide each term of the original expression by the GCF:
- First term:
[tex]\(\frac{40x^4y^3}{5x^3y} = 8xy^2\)[/tex]
- Second term:
[tex]\(\frac{-25x^3y}{5x^3y} = -5\)[/tex]
3. Write the Factored Expression:
Combine the GCF with the simplified terms inside parentheses:
[tex]\[
40x^4y^3 - 25x^3y = 5x^3y(8xy^2 - 5)
\][/tex]
Therefore, the factored form of the expression is [tex]\(5x^3y(8xy^2 - 5)\)[/tex].
1. Identify the Greatest Common Factor (GCF):
Look for common factors in the coefficients and the variables from both terms.
- Coefficients: The numbers are 40 and 25. The GCF of 40 and 25 is 5.
- Variables:
- For [tex]\(x^4\)[/tex] and [tex]\(x^3\)[/tex], the common factor is [tex]\(x^3\)[/tex].
- For [tex]\(y^3\)[/tex] and [tex]\(y\)[/tex], the common factor is [tex]\(y\)[/tex].
Combine these to find the overall GCF: [tex]\(5x^3y\)[/tex].
2. Factor Out the GCF:
Divide each term of the original expression by the GCF:
- First term:
[tex]\(\frac{40x^4y^3}{5x^3y} = 8xy^2\)[/tex]
- Second term:
[tex]\(\frac{-25x^3y}{5x^3y} = -5\)[/tex]
3. Write the Factored Expression:
Combine the GCF with the simplified terms inside parentheses:
[tex]\[
40x^4y^3 - 25x^3y = 5x^3y(8xy^2 - 5)
\][/tex]
Therefore, the factored form of the expression is [tex]\(5x^3y(8xy^2 - 5)\)[/tex].
