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Video: Simplifying Algebraic Expressions

Kathryn Kingham

Simplify (3𝑥 + 4)².

01:55

Video Transcript

Simplify three π‘₯ plus four squared.

Three π‘₯ plus four squared means that we’re going to multiply three π‘₯ plus four times three π‘₯ plus four. Like this. Here we’ll need to multiply our three π‘₯ by three π‘₯ plus four. And we’ll need to multiply our four by three π‘₯ and four.

Starting with three π‘₯ times three π‘₯, that gives us nine π‘₯ squared. Then we multiply three π‘₯ by four, which gives us plus 12π‘₯. From here, we multiply four times three π‘₯, which gives us another 12π‘₯. Finally, we’ll multiply four times four, which gives us 16.

But before we finish, we need to ask ourselves can we combine any like terms to make sure we have this in the simplest form. We only have one π‘₯ squared term, so we just bring that down. But 12π‘₯ and 12π‘₯ can be added together, giving us 24π‘₯.

So yes, there were some terms we could combine, because there’s nothing we can combine with the 16. We just bring it down. And there we have the simplified form of the expression three π‘₯ plus four squared. It would be nine π‘₯ squared plus 24π‘₯ plus 16.