(2a-5b)^2

Jasonbradley

2 min read

·

Jun 16, 2024

9

Share

Expanding (2a - 5b)^2

The expression (2a - 5b)^2 represents the square of a binomial, which is a polynomial with two terms. To expand this expression, we can use the following formula:

(a - b)^2 = a^2 - 2ab + b^2

Applying the Formula:

1. Identify a and b: In our case, a = 2a and b = 5b.

2. Substitute into the formula: (2a - 5b)^2 = (2a)^2 - 2(2a)(5b) + (5b)^2

3. Simplify: (2a - 5b)^2 = 4a^2 - 20ab + 25b^2

Therefore, the expanded form of (2a - 5b)^2 is 4a^2 - 20ab + 25b^2.

Key Points:

• Remember that squaring a binomial means multiplying it by itself.
• The formula (a - b)^2 = a^2 - 2ab + b^2 is a useful shortcut for expanding binomials.
• Be careful with the signs in the formula. The middle term is always negative.

Example:

Let's say we want to find the value of (2a - 5b)^2 when a = 3 and b = 2.

1. Substitute the values: 4(3)^2 - 20(3)(2) + 25(2)^2
2. Simplify: 36 - 120 + 100 = 16

Therefore, when a = 3 and b = 2, (2a - 5b)^2 equals 16.