Multiply polynomials

key notes:

To simplify the product of two binomials, use the distributive property.

As a shortcut, you can use the FOIL method. Find the products of the First, Outside, Inside, and Last terms, and then add them.

Square of a binomial:

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

To multiply powers with the same base, add their exponents.

Learn with an example

🔔 Find the product.

Simplify your answer.

(u+4)(3u+3)

Use the distributive property to simplify (u+4)(3u+3). You can use the FOIL method:

Multiply the first terms of (u+4)(3u+3):

(u)(3u)=3u2

Multiply the outside terms of (u+4)(3u+3):

(u)(3)=3u

Multiply the inside terms of (u+4)(3u+3):

(4)(3u)=12u

Multiply the last terms of (u+4)(3u+3):

(4)(3)=12

Finally, add these results and simplify.

3u2+3u+12u+12

3u2+15u+12

🔔 Find the square.

Simplify your answer.

(3m–1)2

(3m–1)2 is the square of a binomial, just like (a–b)2. So, you can find (3m–1)2 with this formula:

(a–b)2=a2–2ab+b2

Replace a with 3m and b with –1, then simplify.

(3m–1)2

(3m)2–2(3m)(1)+12

9m2–6m+1

🔔 Find the product.

Simplify your answer.

–3u2(3u2+2u)

Find the product.

–3u2(3u2+2u)

–3u2(3u2)+–3u2(2u) Apply the distributive property

–9u4+–6u3 Simplify

–9u4–6u3 Rewrite as subtraction

let’s practice!🖊️