### Video Transcript

Expand negative two 𝑥 squared
times 𝑥 to the fourth power plus 𝑥 squared.

In this question, we are asked to
expand a given algebraic expression. To do this, we can note that the
given expression is a product of a single term with an expression with two
terms. We can expand this expression by
recalling the distributive property of multiplication over addition, which tells us
𝑎 times 𝑏 plus 𝑐 is equal to 𝑎𝑏 plus 𝑎𝑐. To apply this to the given
expression, we can set 𝑎 equal to negative two 𝑥 squared, 𝑏 equal to 𝑥 to the
fourth power, and 𝑐 equal to 𝑥 squared.

However, it is often easier to
think of the distribution process as just multiplying every term inside the
parentheses by the factor outside. This gives us negative two 𝑥
squared times 𝑥 to the fourth power plus negative two 𝑥 squared multiplied by 𝑥
squared. We can simplify this expression by
recalling that multiplication is associative, so we can evaluate the product in any
order. We can then use the product rule
for exponents, which we recall tells us that 𝑥 to the power of 𝑛 times 𝑥 to the
power of 𝑚 equals 𝑥 to the power of 𝑛 plus 𝑚.

Applying this to each term
separately gives us negative two 𝑥 to the power of two plus four minus two 𝑥 to
the power of two plus two. Evaluating the sum in each exponent
then gives us negative two 𝑥 to the sixth power minus two 𝑥 to the fourth power,
which is our final answer.