Multiply two binomials: special cases

Difference of squares:

(a+b)(a–b)=a2–b2

Square of a binomial:

  • (a+b)2=a2+2ab+b2
  • (a–b)2=a2–2ab+b2

Learn with an example

Simplify your answer.

(2v+2)(2v–2)

(2v+2)(2v–2) is the difference of squares, just like (a+b)(a–b). So, you can find (2v+2)(2v–2) with this formula:

(a+b)(a–b)=a2–b2

Replace a with 2v and b with 2, then simplify.

(2v+2)(2v–2)

(2v)2–22

4v2–4

Simplify your answer.

(d+3)(d–3)

(d+3)(d–3) is the difference of squares, just like (a+b)(a–b). So, you can find (d+3)(d–3) with this formula:

(a+b)(a–b)=a2–b2

Replace a with d and b with 3, then simplify.

(d+3)(d–3)

d2–32

d2–9

Simplify your answer.

(2k+3)2

(2k+3)2 is the square of a binomial, just like (a+b)2. So, you can find (2k+3)2 with this formula:

(a+b)2=a2+2ab+b2

Replace a with 2k and b with 3, then simplify.

(2k+3)2

(2k)2+2(2k)(3)+32

4k2+12k+9

let’s practice!šŸ–Šļø