(2x-7)^2

Jasonbradley

2 min read

·

Jun 16, 2024

8

Share

Expanding (2x - 7)^2

The expression (2x - 7)^2 represents the square of a binomial. To expand this, we can apply the FOIL method or use the square of a difference pattern.

Using the FOIL method

FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials by systematically considering all possible product combinations.

1. First: Multiply the first terms of each binomial: (2x) * (2x) = 4x^2
2. Outer: Multiply the outer terms of the binomials: (2x) * (-7) = -14x
3. Inner: Multiply the inner terms of the binomials: (-7) * (2x) = -14x
4. Last: Multiply the last terms of each binomial: (-7) * (-7) = 49

Now, we combine the terms: 4x^2 - 14x - 14x + 49

Finally, simplify by combining the like terms: 4x^2 - 28x + 49

Using the Square of a Difference Pattern

The square of a difference pattern states: (a - b)^2 = a^2 - 2ab + b^2

Applying this to our expression:

• a = 2x
• b = 7

Substituting these values into the pattern:

(2x)^2 - 2(2x)(7) + 7^2 = 4x^2 - 28x + 49

Therefore, both methods lead to the same expanded form: 4x^2 - 28x + 49

This expanded form represents a quadratic expression which can be further manipulated or used in different mathematical contexts.