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Factoring
Factoring Perfect Trinomial Squares

Recognizing that a binomial is a difference of perfect squares or that a trinomial is a perfect square can save time if you have to factor it.

 Difference of perfect squares: Perfect trinomial squares: x2-y2=(x-y)(x+y) x2+2xy+y2=(x+y)2 x2-2xy+y2=(x-y)2

To factor a difference of perfect squares:

1. Find the quantity that was squared (multiplied by itself) to give the first square and the quantity that was squared to give the second square.
2. Write the sum of the two quantities as the first factor and the difference of the two quantities as the second factor.

Factor x2-16
x2-16=x2-42=(x-4)(x+4)

Factor 8x2-32
8x2-32=8(x2-4)=8(x-2)(x+2)

To factor a perfect trinomial square:

1. Find the quantity that were squared to give the two squares in the trinomial.
2. Connect the two quantities with the sign of the remaining term.
3. Indicate that the resulting binomial is to be used twice as a factor.

Factor a2+8a+16
a2+8a+16=a2+8a+42=(a+4)(a+4)=(a+4)2

If the area of a perfect square is 49m2+28m+4, find the side length.

To find the side length we have to factor 49m2+28m+4. That is:

49m2+28m+4=(7m)2+28m+(2)2=(7m+2)2

The side length is 7m+2 units.