Question

Fully explain why, in general, (a + b)^2 = a^2 +b^2.

Answer 1

Below!

Explanation:

Let's simplify each side to determine if both sides are equal.

Left hand side of the equation:

• Expression: (a + b)²

This expression can be simplified using the rule (x + y)² = x² + 2(x)(y) + y².

• ⇒ a² + 2(a)(b) + b²

When opening the parenthesis, we get;

• ⇒ a² + 2ab + b²

This expression cannot be simplified further as there are no like terms in the expression obtained.

Right hand side of the equation:

• Expression: a² + b²

This expression cannot be simplified further as there are no like terms in the expression obtained.

Given equation:

• (a + b)² = a² + b²

This can be rewritten as;

• a² + 2ab + b² = a² + b² (False)

Therefore, it is impossible for a² + b² to be equivalent to a² + 2ab + b².

Answer 2

No this is not correct identity

• (a+b)²
• (a+b)(a+b)
• a(a+b)+b(a+b)
• a²+ab+ba+b²
• a²+2ab+b²

Hence it's wrong