Video Transcript
Expand two 𝑥 plus five
squared.
We’re asked to expand the square of
a binomial. We can do this by first recalling
that squaring an expression means multiplying that expression by itself. So, two 𝑥 plus five squared is
equal to two 𝑥 plus five times two 𝑥 plus five. We can now expand this product by
distributing the first factor over every term in the second factor. So, we multiply two 𝑥 by two 𝑥
plus five and five by two 𝑥 plus five. This is written as two 𝑥 times two
𝑥 plus five plus five times two 𝑥 plus five. Then, we expand each term by
distributing the factor over each binomial, like so: two 𝑥 times two 𝑥 plus two 𝑥
times five plus five times two 𝑥 plus five times five.
We can now simplify each term by
recalling that 𝑥 times 𝑥 is equal to 𝑥 squared and collecting like terms. So we have four 𝑥 squared plus
10𝑥 plus 10𝑥 plus 25, which simplifies to four 𝑥 squared plus 20𝑥 plus 25. This is the square of two 𝑥 plus
five.
We can also answer this question by
recalling that we can square a binomial using the formula 𝑎 plus 𝑏 squared equals
𝑎 squared plus two 𝑎𝑏 plus 𝑏 squared. Substituting 𝑎 equals two 𝑥 and
𝑏 equals five into the formula yields two 𝑥 squared plus two times two 𝑥 times
five plus five squared, which simplifies to four 𝑥 squared plus 20𝑥 plus 25.
