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].

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Rewritten by : Barada