Question Video: Expanding and Simplifying Algebraic Expressions Mathematics • First Year of Preparatory School

Video Transcript

Expand and simplify 𝑥 plus two multiplied by 𝑥 plus two.

The expression we need to simplify is the product of two binomials: 𝑥 plus two and 𝑥 plus two. To expand this product means we need to multiply out the brackets. We can do this in a number of different ways, such as using the vertical method or grid method. But the method we’re going to demonstrate here is to take a systematic approach to ensuring we multiply each term in the first binomial by each term in the second.

We begin by multiplying the first term in each binomial together: 𝑥 multiplied by 𝑥, which is 𝑥 squared. Then, we multiply the first term in the first binomial by the second term in the second. This is also known as multiplying the terms on the outside of the product together. 𝑥 multiplied by two is two 𝑥. Next, we multiply the terms on the inside of the product together: two multiplied by 𝑥, which is two 𝑥. And finally we multiply the last term in each binomial together: two multiplied by two, which is four.

At this stage, we have four terms in the expansion, as we should when multiplying the two terms of one binomial by the two terms of another. We can then simplify this expression by combining the like terms in the center. Two 𝑥 plus two 𝑥 is four 𝑥. We’ve therefore found that the expanded and simplified form of 𝑥 plus two multiplied by 𝑥 plus two is 𝑥 squared plus four 𝑥 plus four.

It’s worth pointing out that the product we’ve simplified here is, in fact, a perfect square, as both factors are the same. When we expand a perfect square of the form 𝑥 plus 𝑎 squared, we obtain the simplified expression 𝑥 squared plus two 𝑎𝑥 plus 𝑎 squared. Here, the value of 𝑎 is two, and we can confirm that the coefficient of 𝑥 is indeed equal to two times two. And the constant term, four, is indeed equal to two squared.