At the end of this lesson, students will be able to:
- Find the square of a binomial.
- Find the product of binomials using sum and difference formula.
- Solve problems using special products of polynomials.
Terms introduced in this lesson:
square of a binomial, binomial square
sum and difference of terms
difference of squares
Teaching Strategies and Tips
In this lesson, students learn about special products of binomials.
- Have students learn to recognize the basic patterns.
- In classroom examples, use colors to denote the numbers playing the role of a and b in the formulas.
In the special formulas, point out that b is considered positive; the sign does not go with the term.
Square the binomial.
The minus sign tells us to use (a−b)2=a2−2ab+b2. Setting a=x and b=3 (and not −3),
General Tip: Students commit a very common error when they write, for example, (x+y)2=x2+y2; that is, they distribute the exponent over addition instead of multiplication.
- The power rule for products does not apply to sums or differences within the parentheses. In general, (xn+ym)p≠xnp+ymp.
- Students can learn to avoid this mistake by recalling the exponent definition. Therefore, a polynomial raised to an exponent means that the polynomial is multiplied by itself as many times as the exponent indicates. For example:
- See Review Questions 1-4, especially Problem 4.