# Binomial Expansion Using Pascal’s Triangle

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As an online math tutor, I love teaching my students helpful shortcuts! Algebra 2 and Precalculus students, this one is for you. Let’s learn a binomial expansion shortcut. Let’s say we want to expand \$(x+2)^3\$.

Without knowing a shortcut, we would start out by first writing this as \$(x+2)(x+2)(x+2)\$. Then we could FOIL the first two terms.

\$(x+2)^3\$
\$=(x+2)(x+2)(x+2)\$
\$=(x^2+4x+4)(x+2)\$

Which gets us closer, but now we need to multiply these together (by multiplying everything in the first polynomial by everything in the second polynomial).

\$=(x^2+4x+4)(x+2)\$
\$=(x^3+2x^2+4x^2+8x+4x+8)\$
\$=(x^3+6x^2+12x+8)\$

Phew, we’re done. But what if we wanted to expand a binomial that has an exponent of 4 or 5? Multiplying all of those terms together can really make your head start spinning.

Luckily, there’s an easier way. We can use Pascal’s Triangle to expand binomials. Check out my video for four examples of using Pascal’s triangle to expand binomials.

-Katie, the online math tutor