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Chapter 8: Problem 150

Expand \((x+3 y-5 t)^{2}\)

Short Answer

Expert verified
The expanded form of the given expression \((x+3y-5t)^2\) is \(x^{2} + 9y^{2} + 25t^{2} + 6xy - 10xt - 30yt\).

Step by step solution

01

Identify the terms

In the given expression \((x+3y-5t)^2\), the terms are a = x, b = 3y, and c = -5t.
02

Compute the squares of individual terms

According to the formula, we need to compute the squares of each term: - \(a^2 = x^2\) - \(b^2 = (3y)^2 = 9y^2\) - \(c^2 = (-5t)^2 = 25t^2\)
03

Compute the products of the terms

Next, we need to calculate the twice the product of each pair of different terms: - \(2ab = 2(x)(3y) = 6xy\) - \(2ac = 2(x)(-5t) = -10xt\) - \(2bc = 2(3y)(-5t) = -30yt\)
04

Combine the results

Finally, we add up the results from Step 2 and Step 3: \((x+3y-5t)^2 = x^2 + 9y^2 + 25t^2 + 6xy - 10xt - 30yt\) So, the expanded form of the given expression is \((x+3y-5t)^2 = x^{2} + 9y^{2} + 25t^{2} + 6xy - 10xt - 30yt\).

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