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Rewrite and complete the expression:

[tex]\[
\begin{array}{l}
(20x^2 - 12x) + (25x - 15) \\
4x(5x - 3) + 5(5x - 3) \\
(5x - 3)(4x + 5)
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
To solve the expression [tex]\((20x^2 - 12x) + (25x - 15)\)[/tex], we will factor it step by step.

1. Group the terms:
[tex]\[ (20x^2 - 12x) + (25x - 15) \][/tex]

2. Factor out the greatest common factor (GCF) from each group:
- For the first group: [tex]\(20x^2 - 12x\)[/tex], the GCF is [tex]\(4x\)[/tex].
[tex]\[ 20x^2 - 12x = 4x(5x - 3) \][/tex]
- For the second group: [tex]\(25x - 15\)[/tex], the GCF is [tex]\(5\)[/tex].
[tex]\[ 25x - 15 = 5(5x - 3) \][/tex]

3. Rewrite the expression with the factored terms:
[tex]\[ (20x^2 - 12x) + (25x - 15) = 4x(5x - 3) + 5(5x - 3) \][/tex]

4. Notice that both terms have a common factor of [tex]\((5x - 3)\)[/tex]:
- Factor out the common factor [tex]\((5x - 3)\)[/tex] from both terms.
[tex]\[ 4x(5x - 3) + 5(5x - 3) = (5x - 3)(4x + 5) \][/tex]

So, the fully factored form of the expression [tex]\((20x^2 - 12x) + (25x - 15)\)[/tex] is:
[tex]\[ (5x - 3)(4x + 5) \][/tex]

Therefore, the final answer is:
[tex]\[ (5x - 3)(4x + 5) \][/tex]
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