a + b whole square is what

Step 1: Understand the notation

The notation $(a+b)^2$ means that the expression $(a+b)$ is multiplied by itself. The exponent $2$ indicates that the base, which is $(a+b)$, should be multiplied by itself $2$ times.

Step 2: Rewrite the expression as repeated multiplication

Based on the definition of squaring, we can rewrite $(a+b)^2$ as the product of $2$ identical binomials: $(a+b)$ multiplied by $(a+b)$.

Step 3: Apply the distributive property

To expand the product of $2$ binomials, we apply the distributive property. Each term in the first parenthesis multiplies every term in the second parenthesis, giving $4$ individual products.

Step 4: Simplify each individual term

Now we simplify each term. $a \cdot a$ equals $a^2$, $a \cdot b$ equals $ab$, and by the commutative property of multiplication, $b \cdot a = ab$. Finally, $b \cdot b$ equals $b^2$.

Step 5: Combine like terms

Finally, we combine the like terms $ab$ and $ab$. Adding $1ab$ to $1ab$ yields $2ab$, giving the fundamental algebraic identity $(a+b)^2 = a^2 + 2ab + b^2$.

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