Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Ask your questions and receive precise answers from experienced professionals across different disciplines. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To find the product of [tex]\((5x + 1)(5x - 1)\)[/tex], let's expand the expression using the distributive property (also known as the FOIL method, which stands for First, Outside, Inside, Last):
1. First: Multiply the first terms in each binomial:
[tex]\[ (5x) \cdot (5x) = 25x^2 \][/tex]
2. Outside: Multiply the outer terms in the binomials:
[tex]\[ (5x) \cdot (-1) = -5x \][/tex]
3. Inside: Multiply the inner terms in the binomials:
[tex]\[ 1 \cdot (5x) = 5x \][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[ 1 \cdot (-1) = -1 \][/tex]
Now, add all the products together:
[tex]\[ 25x^2 - 5x + 5x - 1 \][/tex]
Notice that the [tex]\(-5x\)[/tex] and [tex]\(5x\)[/tex] terms cancel each other out:
[tex]\[ 25x^2 - 1 \][/tex]
So, the correct product of [tex]\((5x + 1)(5x - 1)\)[/tex] is:
[tex]\[ 25x^2 - 1 \][/tex]
Therefore, the correct answer is:
D. [tex]\( 25x^2 - 1 \)[/tex]
1. First: Multiply the first terms in each binomial:
[tex]\[ (5x) \cdot (5x) = 25x^2 \][/tex]
2. Outside: Multiply the outer terms in the binomials:
[tex]\[ (5x) \cdot (-1) = -5x \][/tex]
3. Inside: Multiply the inner terms in the binomials:
[tex]\[ 1 \cdot (5x) = 5x \][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[ 1 \cdot (-1) = -1 \][/tex]
Now, add all the products together:
[tex]\[ 25x^2 - 5x + 5x - 1 \][/tex]
Notice that the [tex]\(-5x\)[/tex] and [tex]\(5x\)[/tex] terms cancel each other out:
[tex]\[ 25x^2 - 1 \][/tex]
So, the correct product of [tex]\((5x + 1)(5x - 1)\)[/tex] is:
[tex]\[ 25x^2 - 1 \][/tex]
Therefore, the correct answer is:
D. [tex]\( 25x^2 - 1 \)[/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.