We have seen how to multiply two binomials in
"Product of Two Binomials" . In this section, we learn how to
multiply a binomial (expression with two terms) by a trinomial (expression withthree terms). Fortunately, we use the same methods we used to multiply two
binomials to multiply a binomial and a trinomial.
For example, multiply
by
.
Multiplication of Binomial with Trinomial
If the binomial is
and the trinomial is
, then the very first step is to apply the distributive law:
If you remember this, you will never go wrong!
Multiply
with
.
We are given two expressions: a binomial,
, and a trinomial,
. We need to multiply them together.
Apply the distributive law and then simplify the resulting expression.
The product of
and
is
.
Find the product of
and
.
We are given two expressions: a binomial,
, and a trinomial,
.
We need to multiply them together.
Apply the distributive law and then simplify the resulting expression.
The product of
and
is
.
We have seen that:
This is known as a
sum of cubes .
Investigation : difference of cubes
Show that the difference of cubes
(
) is given by the product of
and
.
Products
Find the products of:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
(p)
(q)
(r)
(s)
(t)
Factorising a quadratic
Khan academy video on factorising a quadratic.
Factorisation can be seen as the reverse of calculating the product of factors. In order to factorise a quadratic, we need to find the factors which when multiplied together equal the original quadratic.
