use foil to explain how to find the product of (a + b)(a - b). then describe a shortcut that you could use…

Explanation:

Step1: Apply FOIL method

F: First terms: $a\times a=a^{2}$ O: Outer terms: $a\times(-b)=-ab$ I: Inner terms: $b\times a = ab$ L: Last terms: $b\times(-b)=-b^{2}$ Then $(a + b)(a - b)=a^{2}-ab + ab - b^{2}$

Step2: Simplify the result

Combine like - terms: $-ab+ab = 0$, so $(a + b)(a - b)=a^{2}-b^{2}$

Step3: Short - cut explanation

The product of $(a + b)(a - b)$ is the difference of squares. The formula for the difference of squares is $(x + y)(x - y)=x^{2}-y^{2}$. Here $x = a$ and $y = b$. So directly we can get $(a + b)(a - b)=a^{2}-b^{2}$

Answer:

Using FOIL: $(a + b)(a - b)=a^{2}-ab + ab - b^{2}=a^{2}-b^{2}$. Short - cut: The product of $(a + b)(a - b)$ is given by the difference of squares formula $(x + y)(x - y)=x^{2}-y^{2}$, so $(a + b)(a - b)=a^{2}-b^{2}$