Algebra 1 / Unit 8: Polynomials and Factoring
8.3 Special Products
Notes
Three patterns save time:
- Square of a sum: $(a + b)^2 = a^2 + 2ab + b^2$
- Square of a difference: $(a - b)^2 = a^2 - 2ab + b^2$
- Sum times difference: $(a + b)(a - b) = a^2 - b^2$
- Common mistake: $(x + 3)^2$ is not $x^2 + 9$. You need the middle term $6x$.
Practice
$(x + 5)^2 =$
$a^2 + 2ab + b^2$ with $a = x$, $b = 5$.
$(3y - 2)^2 =$
$9y^2 - 2(3y)(2) + 4$.
$(x + 7)(x - 7) =$
Sum times difference: $a^2 - b^2$.
Ready for more? Take the Unit 8 test.