(3x-1)^2 Expand

Jasonbradley

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Jun 16, 2024

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Expanding (3x-1)^2

The expression (3x-1)^2 represents the square of the binomial (3x-1). To expand it, we can use the FOIL method or the square of a binomial formula.

Using FOIL Method

FOIL stands for First, Outer, Inner, Last. It helps us multiply two binomials by systematically multiplying each term in the first binomial with each term in the second binomial.

1. First: Multiply the first terms of each binomial: (3x)(3x) = 9x²
2. Outer: Multiply the outer terms of the binomials: (3x)(-1) = -3x
3. Inner: Multiply the inner terms of the binomials: (-1)(3x) = -3x
4. Last: Multiply the last terms of each binomial: (-1)(-1) = 1

Now, add all the terms together: 9x² - 3x - 3x + 1

Combining like terms, we get the expanded form: 9x² - 6x + 1

Using Square of a Binomial Formula

The square of a binomial formula states: (a - b)² = a² - 2ab + b²

In our case, a = 3x and b = 1. Substituting these values into the formula, we get:

(3x - 1)² = (3x)² - 2(3x)(1) + (1)²

Simplifying the expression: 9x² - 6x + 1

Therefore, the expanded form of (3x-1)² is 9x² - 6x + 1.

Both methods give us the same result, demonstrating the versatility of these algebraic tools in simplifying and expanding expressions.