Questions: Find the product: (8 v w-5 t)^2 Select the best answer from the choices provided. A. 64 v^2 w^2+25 t^2 B. 64 v^2 w^2-40 t v w+25 t^2 C. 64 v^2 w^2-80 t v w+25 t^2 D. 64 v^2 w^2+80 t v w+25 t^2

Find the product: (8 v w-5 t)^2 Select the best answer from the choices provided. A. 64 v^2 w^2+25 t^2 B. 64 v^2 w^2-40 t v w+25 t^2 C. 64 v^2 w^2-80 t v w+25 t^2 D. 64 v^2 w^2+80 t v w+25 t^2
Transcript text: Find the product: \[ (8 v w-5 t)^{2} \] Select the best answer from the choices provided. A. $64 v^{2} w^{2}+25 t^{2}$ B. $64 v^{2} w^{2}-40 t v w+25 t^{2}$ C. $64 v^{2} w^{2}-80 t v w+25 t^{2}$ D. $64 v^{2} w^{2}+80 t v w+25 t^{2}$
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Solution

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Solution Steps

To find the product of \((8vw - 5t)^2\), we need to use the formula for the square of a binomial, which is \((a - b)^2 = a^2 - 2ab + b^2\). Here, \(a = 8vw\) and \(b = 5t\). We will apply this formula to expand the given expression.

Step 1: Expand the Binomial

To expand the expression \((8vw - 5t)^2\), we apply the binomial expansion formula: \[ (a - b)^2 = a^2 - 2ab + b^2 \] where \(a = 8vw\) and \(b = 5t\).

Step 2: Calculate Each Term

Calculating each term:

  • The first term is: \[ (8vw)^2 = 64v^2w^2 \]
  • The second term is: \[ -2(8vw)(5t) = -80tvw \]
  • The third term is: \[ (5t)^2 = 25t^2 \]
Step 3: Combine the Terms

Combining all the terms, we have: \[ (8vw - 5t)^2 = 64v^2w^2 - 80tvw + 25t^2 \]

Final Answer

Thus, the expanded form of the expression is: \[ \boxed{64v^2w^2 - 80tvw + 25t^2} \]

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