Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To solve the given equation [tex]\((xyz)^2 - 1 = \square \cdot (xyz - 1)\)[/tex], we start by utilizing the algebraic identity known as the difference of squares.
The difference of squares states that:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
Let's rewrite our given expression in a way that can exploit this identity. We'll set [tex]\(a = xyz\)[/tex] and [tex]\(b = 1\)[/tex]. We have:
[tex]\[ (xyz)^2 - 1^2 = (xyz - 1)(xyz + 1) \][/tex]
Now, compare the left-hand side of the given equation with this identity. The left-hand side [tex]\((xyz)^2 - 1\)[/tex] matches [tex]\(a^2 - b^2\)[/tex], where [tex]\(a = xyz\)[/tex] and [tex]\(b = 1\)[/tex].
According to the difference of squares identity:
[tex]\[ (xyz)^2 - 1 = (xyz - 1)(xyz + 1) \][/tex]
This shows that the expression on the right-hand side, [tex]\(\square\)[/tex], must be [tex]\(xyz + 1\)[/tex] to match the structure of the difference of squares identity.
Therefore, the completed equation looks like:
[tex]\[ (xyz)^2 - 1 = (xyz + 1) \cdot (xyz - 1) \][/tex]
Hence, the expression that correctly completes the provided equation is:
[tex]\[ (xyz + 1) \][/tex]
The difference of squares states that:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
Let's rewrite our given expression in a way that can exploit this identity. We'll set [tex]\(a = xyz\)[/tex] and [tex]\(b = 1\)[/tex]. We have:
[tex]\[ (xyz)^2 - 1^2 = (xyz - 1)(xyz + 1) \][/tex]
Now, compare the left-hand side of the given equation with this identity. The left-hand side [tex]\((xyz)^2 - 1\)[/tex] matches [tex]\(a^2 - b^2\)[/tex], where [tex]\(a = xyz\)[/tex] and [tex]\(b = 1\)[/tex].
According to the difference of squares identity:
[tex]\[ (xyz)^2 - 1 = (xyz - 1)(xyz + 1) \][/tex]
This shows that the expression on the right-hand side, [tex]\(\square\)[/tex], must be [tex]\(xyz + 1\)[/tex] to match the structure of the difference of squares identity.
Therefore, the completed equation looks like:
[tex]\[ (xyz)^2 - 1 = (xyz + 1) \cdot (xyz - 1) \][/tex]
Hence, the expression that correctly completes the provided equation is:
[tex]\[ (xyz + 1) \][/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.