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Binomial special products review

A review of the difference of squares pattern (a+b)(a-b)=a^2-b^2, as well as other common patterns encountered while multiplying binomials, such as (a+b)^2=a^2+2ab+b^2.
These types of binomial multiplication problems come up time and time again, so it's good to be familiar with some basic patterns.
The "difference of squares" pattern:
(a+b)(ab)=a2b2
Two other patterns:
(a+b)2=a2+2ab+b2(ab)2=a22ab+b2

Example 1

Expand the expression.
(c5)(c+5)
The expression fits the difference of squares pattern:
(a+b)(ab)=a2b2
So our answer is:
(c5)(c+5)=c225
But if you don't recognize the pattern, that's okay too. Just multiply the binomials as normal. Over time, you'll learn to see the pattern.
(c5)(c+5)=c(c)+c(5)5(c)5(5)=c(c)+5c5c5(5)=c225
Notice how the "middle terms" cancel.
Want another example? Check out this video.

Example 2

Expand the expression.
(m+7)2
The expression fits this pattern:
(a+b)2=a2+2ab+b2
So our answer is:
(m+7)2=m2+14m+49
But if you don't recognize the pattern, that's okay too. Just multiply the binomials as normal. Over time, you'll learn to see the pattern.
(m+7)2=(m+7)(m+7)=m(m)+m(7)+7(m)+7(7)=m(m)+7m+7m+7(7)=m2+14m+49
Want another example? Check out this video.

Example 3

Expand this expression.
(6wy)(6w+y)
The expression fits the difference of squares pattern:
(a+b)(ab)=a2b2
So our answer is:
(6wy)(6w+y)=(6w)2y2=36w2y2
But if you don't recognize the pattern, that's okay too. Just multiply the binomials as normal. Over time, you'll learn to see the pattern.
(6wy)(6w+y)=6w(6w)+6w(y)y(6w)y(y)=6w(6w)+6wy6wyy(y)=36w2y2
Notice how the "middle terms" cancel.
Want more practice? Check out this intro exercise and this slightly harder exercise.