please explain what a + b the whole squares
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Step-by-Step Solution
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 two times.
Step 2: Rewrite the expression
Based on the definition of squaring, we can rewrite (a+b)2 as the product of two identical binomials: (a+b) multiplied by (a+b).
Step 3: Apply the distributive property (FOIL method)
To expand the product of two binomials, we use the distributive property. This is often remembered by the acronym FOIL (First, Outer, Inner, Last). We multiply the first terms, then the outer terms, then the inner terms, and finally the last terms.
Step 4: Simplify the terms
Now, we simplify each product. a⋅a becomes a2, a⋅b is ab, b⋅a is ba (which is the same as ab), and b⋅b becomes b2.
Step 5: Combine like terms
Finally, we combine the like terms. The terms ab and ab are like terms, so adding them together gives 2ab. This results in the well-known algebraic identity for the square of a binomial.