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

Explanation:

Step1: First terms

Multiply the first terms of each binomial: (a\times a=a^{2})

Step2: Outer terms

Multiply the outer terms: (a\times(-b)=-ab)

Step3: Inner terms

Multiply the inner terms: (b\times a = ba)

Step4: Last terms

Multiply the last terms: (b\times(-b)=-b^{2})

Step5: Combine like terms

(a^{2}-ab + ab-b^{2}). The (-ab) and (+ab) cancel out, leaving (a^{2}-b^{2})

The shortcut is using the difference - of - squares formula ((x + y)(x - y)=x^{2}-y^{2}). Here (x = a) and (y = b), so ((a + b)(a - b)=a^{2}-b^{2})

Answer:

Using FOIL: ((a + b)(a - b)=a\times a+a\times(-b)+b\times a + b\times(-b)=a^{2}-ab+ab - b^{2}=a^{2}-b^{2}). Shortcut: Use the difference - of - squares formula ((x + y)(x - y)=x^{2}-y^{2}), so ((a + b)(a - b)=a^{2}-b^{2})