At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
To find the completely factored form of the quadratic expression [tex]\(8x^2 - 50\)[/tex], let's break it down step by step.
First, observe that [tex]\(8x^2 - 50\)[/tex] can be written as:
[tex]\[8x^2 - 50\][/tex]
We start by factoring out the greatest common factor (GCF). The GCF of the terms [tex]\(8x^2\)[/tex] and [tex]\(-50\)[/tex] is 2. So, we factor out 2 from the expression:
[tex]\[8x^2 - 50 = 2(4x^2 - 25)\][/tex]
Next, we focus on factoring the expression inside the parentheses: [tex]\(4x^2 - 25\)[/tex]. Notice that this is a difference of squares. Recall the difference of squares formula:
[tex]\[a^2 - b^2 = (a - b)(a + b)\][/tex]
We can apply this formula to [tex]\(4x^2 - 25\)[/tex], where [tex]\(4x^2\)[/tex] is [tex]\((2x)^2\)[/tex] and [tex]\(25\)[/tex] is [tex]\(5^2\)[/tex]:
[tex]\[4x^2 - 25 = (2x)^2 - 5^2\][/tex]
Using the difference of squares formula, we have:
[tex]\[4x^2 - 25 = (2x - 5)(2x + 5)\][/tex]
Finally, substituting back into our original factored form, we get:
[tex]\[8x^2 - 50 = 2(2x - 5)(2x + 5)\][/tex]
Thus, the completely factored form of [tex]\(8x^2 - 50\)[/tex] is:
[tex]\[2(2x - 5)(2x + 5)\][/tex]
So, the correct answer is:
[tex]\[2(2x+5)(2x-5)\][/tex]
First, observe that [tex]\(8x^2 - 50\)[/tex] can be written as:
[tex]\[8x^2 - 50\][/tex]
We start by factoring out the greatest common factor (GCF). The GCF of the terms [tex]\(8x^2\)[/tex] and [tex]\(-50\)[/tex] is 2. So, we factor out 2 from the expression:
[tex]\[8x^2 - 50 = 2(4x^2 - 25)\][/tex]
Next, we focus on factoring the expression inside the parentheses: [tex]\(4x^2 - 25\)[/tex]. Notice that this is a difference of squares. Recall the difference of squares formula:
[tex]\[a^2 - b^2 = (a - b)(a + b)\][/tex]
We can apply this formula to [tex]\(4x^2 - 25\)[/tex], where [tex]\(4x^2\)[/tex] is [tex]\((2x)^2\)[/tex] and [tex]\(25\)[/tex] is [tex]\(5^2\)[/tex]:
[tex]\[4x^2 - 25 = (2x)^2 - 5^2\][/tex]
Using the difference of squares formula, we have:
[tex]\[4x^2 - 25 = (2x - 5)(2x + 5)\][/tex]
Finally, substituting back into our original factored form, we get:
[tex]\[8x^2 - 50 = 2(2x - 5)(2x + 5)\][/tex]
Thus, the completely factored form of [tex]\(8x^2 - 50\)[/tex] is:
[tex]\[2(2x - 5)(2x + 5)\][/tex]
So, the correct answer is:
[tex]\[2(2x+5)(2x-5)\][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.