1 thought on “Write the horizontaldistributive <br /><br />approach, vertical distributive <br /><br />approach, grid approach, foil <br /><br /”
Answer:
Remember that when you multiply a binomial by a binomial you get four terms. Sometimes you can combine like terms to get a trinomial, but sometimes there are no like terms to combine. Let’s look at the last example again and pay particular attention to how we got the four terms.
(
x
+
2
)
(
x
−
y
)
x
2
−
xy
+
2
x
−
2
y
Where did the first term,
x
2
, come from?
It is the product of
x
and
x
, the first terms in
(
x
+
2
)
and
(
x
−
y
)
.
Parentheses x plus 2 times parentheses x minus y is shown. There is a red arrow from the first x to the second. Beside this,
The next term,
−
xy
, is the product of
x
and
−
y
, the two outer terms.
Parentheses x plus 2 times parentheses x minus y is shown. There is a black arrow from the first x to the second x. There is a red arrow from the first x to the y. Beside this,
The third term,
+
2
x
, is the product of
2
and
x
, the two inner terms.
Parentheses x plus 2 times parentheses x minus y is shown. There is a black arrow from the first x to the second x. There is a black arrow from the first x to the y. There is a red arrow from the 2 to the x. Below that,
And the last term,
−
2
y
, came from multiplying the two last terms.
Parentheses x plus 2 times parentheses x minus y is shown. There is a black arrow from the first x to the second x. There is a black arrow from the first x to the y. There is a black arrow from the 2 to the x. There is a red arrow from the 2 to the y. Above that,
We abbreviate “First, Outer, Inner, Last” as FOIL. The letters stand for ‘First, Outer, Inner, Last’. The word FOIL is easy to remember and ensures we find all four products. We might say we use the FOIL method to multiply two binomials.
Answer:
Remember that when you multiply a binomial by a binomial you get four terms. Sometimes you can combine like terms to get a trinomial, but sometimes there are no like terms to combine. Let’s look at the last example again and pay particular attention to how we got the four terms.
(
x
+
2
)
(
x
−
y
)
x
2
−
xy
+
2
x
−
2
y
Where did the first term,
x
2
, come from?
It is the product of
x
and
x
, the first terms in
(
x
+
2
)
and
(
x
−
y
)
.
Parentheses x plus 2 times parentheses x minus y is shown. There is a red arrow from the first x to the second. Beside this,
The next term,
−
xy
, is the product of
x
and
−
y
, the two outer terms.
Parentheses x plus 2 times parentheses x minus y is shown. There is a black arrow from the first x to the second x. There is a red arrow from the first x to the y. Beside this,
The third term,
+
2
x
, is the product of
2
and
x
, the two inner terms.
Parentheses x plus 2 times parentheses x minus y is shown. There is a black arrow from the first x to the second x. There is a black arrow from the first x to the y. There is a red arrow from the 2 to the x. Below that,
And the last term,
−
2
y
, came from multiplying the two last terms.
Parentheses x plus 2 times parentheses x minus y is shown. There is a black arrow from the first x to the second x. There is a black arrow from the first x to the y. There is a black arrow from the 2 to the x. There is a red arrow from the 2 to the y. Above that,
We abbreviate “First, Outer, Inner, Last” as FOIL. The letters stand for ‘First, Outer, Inner, Last’. The word FOIL is easy to remember and ensures we find all four products. We might say we use the FOIL method to multiply two binomials.