(x+y)^2=x^2+y^2 True Or False

2 min read Jun 17, 2024

Is (x + y)² = x² + y²?

This is a common misconception in algebra. The equation (x + y)² = x² + y² is false.

Here's why:

Expanding the Left Side

The left side of the equation, (x + y)², represents squaring the entire binomial (x + y). This means multiplying the binomial by itself:

(x + y)² = (x + y) * (x + y)

To expand this, we use the distributive property (also known as FOIL):

First: x * x = x²
Outer: x * y = xy
Inner: y * x = xy
Last: y * y = y²

Adding these terms together:

(x + y)² = x² + xy + xy + y²

Simplifying:

(x + y)² = x² + 2xy + y²

Comparing the Results

Now we can compare the expanded left side with the right side of the original equation:

Left Side: x² + 2xy + y²
Right Side: x² + y²

As you can see, the two sides are not equal. The left side contains the additional term 2xy.

An Example

Let's try a simple example with numbers:

x = 2
y = 3
Left Side: (2 + 3)² = 5² = 25
Right Side: 2² + 3² = 4 + 9 = 13

As you can see, the left side (25) is not equal to the right side (13).

Conclusion

Therefore, the equation (x + y)² = x² + y² is false. The correct expansion of (x + y)² is x² + 2xy + y². It's important to remember the distributive property when expanding binomials and avoid making this common mistake.