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Chapter 0: Problem 50

Find each product. $$(9-5 x)^{2}$$

Short Answer

Expert verified
The product of the binomial (9-5x)^2 is \( 25x^2 - 90x + 81 \).

Step by step solution

01

Understand the Binomial Theorem

When squaring a binomial \( (a - b)^2 \), the Binomial Theorem tells us it results in \( a^2 - 2ab + b^2 \). We will apply this theorem to expand and simplify the given exercise.
02

Apply the Binomial Theorem

Applying the Binomial Theorem to \( (9 - 5x)^2 \), we can write it as \( (9)^2 - 2*(9)*(5x) + (5x)^2 \).
03

Simplify the Expression

Simplify the expression, resulting in \( 81 - 90x + 25x^2 \).
04

Rewrite the Expression

Finally, we rewrite our expression from highest power to lowest power, resulting in \( 25x^2 - 90x +81 \).

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) toproduce a true statement. $$\left(4 \times 10^{3}\right)+\left(3 \times 10^{2}\right)=4.3 \times 10^{3}$$

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