Question Video: Simplifying Algebraic Expressions by Combining Like Terms Mathematics • First Year of Preparatory School

Video Transcript

Simplify negative four 𝑥 plus eight 𝑦 to the fourth power minus two 𝑧 squared plus 𝑥 minus two 𝑦 to the fourth power minus four 𝑧 squared.

In this question, we’re asked to simplify an algebraic expression with six terms. We can do this by collecting like terms. Recall that like terms have the same variables raised to the same powers. In this question, there are three pairs of like terms. We begin by rewriting our expression so that the like terms are next to each other. We have negative four 𝑥 plus 𝑥 plus eight 𝑦 to the fourth power minus two 𝑦 to the fourth power minus two 𝑧 squared minus four 𝑧 squared. Taking out the shared factor of 𝑥 from the first two terms, we have negative four plus one multiplied by 𝑥.

We can then take out the shared factor of 𝑦 to the fourth power from the next two terms, giving us eight minus two multiplied by 𝑦 to the fourth power. Finally, taking out the shared factor of 𝑧 squared from the last two terms, we have negative two minus four multiplied by 𝑧 squared. As negative four plus one is equal to negative three, eight minus two is equal to six, and negative two minus four equals negative six, our expression simplifies to negative three 𝑥 plus six 𝑦 to the fourth power plus negative six 𝑧 squared, which in turn is equal to negative three 𝑥 plus six 𝑦 to the fourth power minus six 𝑧 squared. This is the original expression written in its simplest form.