Final answer:
To square the binomial (a+b)², multiply the terms following the FOIL method: First, Outer, Inner, and Last, which results in a² + 2ab + b² after combining like terms.
Step-by-step explanation:
To square a binomial such as (a+b)², you need to apply the rule that comes from the distributive property, often referred to as the FOIL method (First, Outer, Inner, Last). When squaring (a+b)², you're essentially multiplying (a+b) by itself: (a+b) * (a+b). Here’s a step-by-step method:
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- Multiply the First terms in each binomial together: a * a = a².
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- Multiply the Outer terms together: a * b.
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- Multiply the Inner terms together: b * a (which is the same as the outer).
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- Multiply the Last terms in each binomial together: b * b = b².
Now combine these results: a² + ab + ba + b². Since ab and ba are like terms, you can add them together.
Finally, the squared binomial is a² + 2ab + b². This is the expanded form of (a+b)².