Question
Find the product (in simplified form) \( (x \sqrt{y}+z)(x \sqrt{y}-z) \) \( x^{2} y+2 z x \sqrt{y}-z^{2} \) \( x^{2} y^{2}-z^{2} \) \( x^{2} y-z^{2} \) \( x^{2} y-2^{2} \)
Ask by Peterson Mccoy. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The product simplifies to \( x^{2}y - z^{2} \).
Solution
Calculate or simplify the expression \( (x \sqrt{y}+z)(x \sqrt{y}-z) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(x\sqrt{y}+z\right)\left(x\sqrt{y}-z\right)\)
- step1: Simplify the product:
\(\left(x\sqrt{y}\right)^{2}-z^{2}\)
- step2: Evaluate the power:
\(x^{2}y-z^{2}\)
The product of \( (x \sqrt{y}+z)(x \sqrt{y}-z) \) is \( x^{2}y-z^{2} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
To find the product of the expression \( (x \sqrt{y}+z)(x \sqrt{y}-z) \), we can use the difference of squares formula, which states that \( (a + b)(a - b) = a^2 - b^2 \). Here, we have: - \( a = x \sqrt{y} \) - \( b = z \) Applying the formula: \[ (x \sqrt{y} + z)(x \sqrt{y} - z) = (x \sqrt{y})^2 - z^2 \] Now, calculate \( (x \sqrt{y})^2 \): \[ (x \sqrt{y})^2 = x^2 y \] Putting it all together gives us: \[ x^2 y - z^2 \] So, the product in simplified form is: \[ \boxed{x^2 y - z^2} \]
