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:
- 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.
- Write the sum of the two quantities as the first factor and the difference of the two quantities as the second factor.
Factor x
2-16
x2-16=x2-42=(x-4)(x+4)
Factor 8x
2-32
8x2-32=8(x2-4)=8(x-2)(x+2)
To factor a perfect trinomial square:
- Find the quantity that were squared to give the two squares in the trinomial.
- Connect the two quantities with the sign of the remaining term.
- Indicate that the resulting binomial is to be used twice as a factor.
Factor a
2+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.
