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:
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.
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.
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:
The side length is 7m+2 units.