Video Transcript
Simplify three 𝑎 cubed minus two
multiplied by two 𝑎 squared plus four.
We’ve been given the product of two
algebraic expressions, each of which are binomials as they each contain two
terms. To simplify this product means we
need to expand the brackets, also known as distributing the parentheses, and then
combine any like terms if possible.
To expand the brackets, we need to
systematically multiply each term in the first binomial by each term in the second
binomial. This will result in four terms. Multiplying the first term in each
binomial together and recalling that when we multiply powers of the same base we add
the exponents gives six 𝑎 to the fifth power. Multiplying the terms on the
outside of the product together gives 12𝑎 cubed. Multiplying the terms on the inside
of the product together gives negative four 𝑎 squared. And finally, multiplying the last
term in each binomial together gives negative eight. This expression can’t be simplified
because the powers of 𝑎 are different in every term.
We’ve therefore found that the
simplified form of three 𝑎 cubed minus two multiplied by two 𝑎 squared plus four
is six 𝑎 to the fifth power plus 12𝑎 cubed minus four 𝑎 squared minus eight.
