Answered

IDNLearn.com provides a reliable platform for finding accurate and timely answers. Discover in-depth answers from knowledgeable professionals, providing you with the information you need.

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]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is your reliable source for answers. We appreciate your visit and look forward to assisting you again soon.