Video Transcript
What does the expression 𝑥 minus two 𝑦 multiplied by 𝑥 plus four 𝑦 multiplied by 𝑥 plus 𝑦 simplify to?
In this question, we have been asked to simplify a product of three binomial terms. We can start by multiplying the first two binomials: 𝑥 minus two 𝑦 and 𝑥 plus four 𝑦. We can do this by using the distributive property of multiplication over addition. We must be careful to remember the negative sign in front of the two 𝑦 term. We can now expand each of the products we are left with, again using the distributive property.
Now, we can combine the like terms, which gives us 𝑥 squared plus two 𝑥𝑦 minus eight 𝑦 squared. Next, we substitute this back into our expression. We are left with a trinomial multiplied by a binomial. We can again expand this using the distributive property. We multiply each of the terms of the trinomial by the binomial, giving us 𝑥 squared lots of 𝑥 plus 𝑦 plus two 𝑥𝑦 lots of 𝑥 plus 𝑦 plus negative eight 𝑦 squared lots of 𝑥 plus 𝑦.
Now, we can multiply each of these terms. Finally, we can combine the like terms. Here, we reach our solution, which is that 𝑥 minus two 𝑦 multiplied by 𝑥 plus four 𝑦 multiplied by 𝑥 plus 𝑦 simplifies to 𝑥 cubed plus three 𝑥 squared 𝑦 minus six 𝑥𝑦 squared minus eight 𝑦 cubed.
