Finding the Sum and Difference of the Same Two Terms
How to Simplify Negative Exponents with Variables
How to Find the Sum of Two Cubes

How to Recognize a Perfectly Squared Binomial

Recognizing a perfectly squared binomial can make life easier. When you recognize a perfectly squared binomial, you've identified a shortcut that saves time when distributing binomials over other terms.

When the same binomial is multiplied by itself — when each of the first two terms is distributed over the second and same terms — the resulting trinomial contains the squares of the two terms and twice their product. For example,

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Example 1: You can see with the following binomial that the same binomial is being multiplied by itself. So, the result of the distribution is the sum of the squares of x and 3 along with twice their product.

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Example 2: Try the binomial distribution, (4y – 5)(4y – 5), which contains negative signs.

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The square of –5 is +25. (Note that the square is positive.)

Twice the product of 4y and –5 is 2(4y)(–5) = –40y

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Example 3: Use the shortcut for the expression,

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where the terms are all variables.

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Example 4: You can use the shortcut even with the expression, [x + (a + b)][x + (a + b)], where parentheses group the last two terms together in this distribution.

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How to Distribute Binomials
When to Distribute or Add First in Algebraic Distribution
How to Distribute Positive and Negative Numbers
How to Distribute Trinomials
How to Distribute with Fractional Powers or Radicals
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