SME
Grade 9 Math · Algebra 1
Adding, subtracting and multiplying polynomials
Use this for “Multiply (2x + 3)(x − 4).”
Diagram
The rectangle’s area is the product: (2x + 3)(x − 4) = 2x² − 5x − 12.
3 positive and negative x tiles cancel as zero pairs.
This is an example. Type your own values to start a new problem.
(
a
x
+
b
)(
c
x
+
(
d
)
)
=
p
x²
+
(
q
)
x
+
(
r
)
Formulas
p
=
a
×
c
2 = 2 × 1
q
=
a
×
d
+
b
×
c
−5 = 2 × (−4) + 3 × 1
r
=
b
×
d
−12 = 3 × (−4)
Assumptions
•
Every term of one factor multiplies every term of the other: four products.
•
The two x terms are like terms: combine them.
•
A negative times a negative is positive.
Step-by-step
WE KNOW
a = 2, b = 3, c = 1, d = −4
FIND
x² coefficient (p), x coefficient (q), number term (r)
Step 1 · Find x² coefficient (p)
Use p = a × c
First terms: ax times cx gives acx².
p
=
2
×
1
p
=
2
Step 2 · Find x coefficient (q)
Use q = a × d + b × c
Outer
and
inner
terms:
ax
times
d
and
b
times
cx
are
both
x
terms,
so
add
them.
q
=
2
×
(−4)
+
3
×
1
q
=
−8
+
3
q
=
−5
Step 3 · Find number term (r)
Use r = b × d
Last terms: the two numbers multiply to the number term.
r
=
3
×
(−4)
r
=
−12
→
2x²
−
5x
−
12
Check
Put the numbers back in. Both sides should match.
2 = 2 × 1 ✓
−5 = 2 × (−4) + 3 × 1 ✓
−12 = 3 × (−4) ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.