Explanation
Definition
The binomial formulas help you expand expressions with parentheses quickly and easily. They consist of three key formulas that you should memorize well. The first formula describes the square of a sum, the second the square of a difference, and the third the product of a sum and a difference of two numbers.
(a+b)^2 = a^2 + 2ab + b^2
(a-b)^2 = a^2 - 2ab + b^2
(a+b)(a-b) = a^2 - b^2
Procedure
Scheme
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Calculate (3+4)^2.
(3+4)^2 = 3^2 + 2 \cdot 3 \cdot 4 + 4^2 = 9 + 24 + 16 = 49
Calculate (5-2)^2.
(5-2)^2 = 5^2 - 2 \cdot 5 \cdot 2 + 2^2 = 25 - 20 + 4 = 9
Calculate (6+2)(6-2).
(6+2)(6-2) = 6^2 - 2^2 = 36 - 4 = 32
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- ★Students often forget that for the 1st and 2nd binomial formulas, the middle term (2ab) must be included.
- ★A common mistake is confusing the 3rd binomial formula with the first two; remember that it has no middle term.
Problems
1 / 3
Calculate using the first binomial formula:
(2+3)^2
2 / 3
Calculate using the second binomial formula:
(7-4)^2
3 / 3
Calculate using the third binomial formula:
(10+5)(10-5)
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