Problem 50 - College Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: Apply the Binomial Theorem

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

Step 3: Simplify the Expression

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

Step 4: Rewrite the Expression

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