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Chapter 0: Problem 49

Find each product. $$(7-2 x)^{2}$$

Short Answer

Expert verified
The product is \(49 - 28x + 4x^2\).

Step by step solution

01

Identify the First Term

The first term (a) in our binomial is 7, so we square this to get \(a^2\), which is \(7^2 = 49\).
02

Identify the Second Term

The second term (b) in our binomial is -2x, so we square this to get \(b^2\), which is \((-2x)^2 = 4x^2\).
03

Identify the Mixed Term

Now we find our mixed term, which is `-2ab`. In this case, `a` is 7 and `b` is -2x, so `-2ab` becomes `2*7*-2x = 28x`.
04

Combine All Terms

Combine all the terms from steps 1 to 3 to get the simplified form of \((7 - 2x)^2\). So, \((7-2x)^2 = 49 - 2*7*2x + 4x^2 = 49 - 28x + 4x^2\).

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