Multiply two binomials: special cases
key notes:
Square of a binomial:
(a+b)2=a2+2ab+b2
(a–b)2=a2–2ab+b2
Difference of squares:
(a+b)(a–b)=a2–b2
Learn with an example
🎯 Find the square.
Simplify your answer.
(3s+2)2
(3s+2)2 is the square of a binomial, just like (a+b)2. So, you can find (3s+2)2 with this formula:
(a+b)2=a2+2ab+b2
Replace a with 3s and b with 2, then simplify.
(3s+2)2
(3s)2+2(3s)(2)+22
9s2+12s+4
🎯 Find the square.
Simplify your answer.
(2f+2)2
(2f+2)2 is the square of a binomial, just like (a+b)2. So, you can find (2f+2)2 with this formula:
(a+b)2=a2+2ab+b2
Replace a with 2f and b with 2, then simplify.
(2f+2)2
(2f)2+2(2f)(2)+22
4f2+8f+4
🎯 Find the product.
Simplify your answer.
(4a–3)(4a+3)
(4a–3)(4a+3) can be written as (4a+3)(4a–3). Either way, it is the difference of squares, just like (a+b)(a–b). So, you can find (4a+3)(4a–3) with this formula:
(a+b)(a–b)=a2–b2
Replace a with 4a and b with 3, then simplify.
(4a+3)(4a–3)
(4a)2–32
16a2 – 9
let’s practice!
