SME
Grade 9 Math · Problem type
Square a binomial
Use this for “(3x − 2)²”.
Diagram
The rectangle’s area is the product: (3x − 2)(3x − 2) = 9x² − 12x + 4.
This is an example. Type your own values to start a new problem.
(
a
x
+
(
b
)
)²
=
p
x²
+
(
q
)
x
+
r
Formulas
p
=
a
2
9
=
3
2
q
=
2
×
a
×
b
−12 = 2 × 3 × (−2)
r
=
b
2
4
=
(−2)
2
Assumptions
•
(ax + b)² means (ax + b)(ax + b), a square of tiles.
•
The middle term is 2abx, from the two equal rectangles: (ax + b)² is not a²x² + b².
Step-by-step
WE KNOW
a = 3, b = −2
FIND
x² coefficient (p), x coefficient (q), number term (r)
Step 1 · Find x² coefficient (p)
Use p = a²
The
x
term
times
itself:
(ax)
2
=
a
2
x
2
.
p
=
3
2
p
=
9
Step 2 · Find x coefficient (q)
Use q = 2 × a × b
The outer and inner products are the same, abx twice.
q
=
2
×
3
×
(−2)
q
=
6
×
(−2)
q
=
−12
Step 3 · Find number term (r)
Use r = b²
The number times itself: always 0 or more.
r
=
(−2)
2
r
=
4
→
9x²
−
12x
+
4
Check
Put the numbers back in. Both sides should match.
9
=
3
2
✓
−12 = 2 × 3 × (−2) ✓
4
=
(−2)
2
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.