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COMMON MATH 1
곱셈공식 · 인수분해 공식 암기용 빈칸 정리
학생들이 직접 빈칸을 채우며 곱셈공식과 인수분해 공식을 암기할 수 있도록 만든 페이지입니다.
출처 · 자료 제작: 두뇌스트레칭
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1. 곱셈공식
1
)
(
a
+
b
)
2
=
a
2
+
□
+
b
2
1)\ (a+b)^2=a^2+\square+b^2
1
)
(
a
+
b
)
2
=
a
2
+
□
+
b
2
2
)
(
a
−
b
)
2
=
a
2
−
□
+
b
2
2)\ (a-b)^2=a^2-\square+b^2
2
)
(
a
−
b
)
2
=
a
2
−
□
+
b
2
3
)
(
a
+
b
)
(
a
−
b
)
=
□
−
□
3)\ (a+b)(a-b)=\square-\square
3
)
(
a
+
b
)
(
a
−
b
)
=
□
−
□
4
)
(
x
+
a
)
(
x
+
b
)
=
x
2
+
□
x
+
□
4)\ (x+a)(x+b)=x^2+\square x+\square
4
)
(
x
+
a
)
(
x
+
b
)
=
x
2
+
□
x
+
□
5
)
(
a
x
+
b
)
(
c
x
+
d
)
=
□
x
2
+
□
x
+
□
5)\ (ax+b)(cx+d)=\square x^2+\square x+\square
5
)
(
a
x
+
b
)
(
c
x
+
d
)
=
□
x
2
+
□
x
+
□
6
)
(
x
+
a
)
(
x
+
b
)
(
x
+
c
)
=
x
3
+
□
x
2
+
□
x
+
□
6)\ (x+a)(x+b)(x+c)=x^3+\square x^2+\square x+\square
6
)
(
x
+
a
)
(
x
+
b
)
(
x
+
c
)
=
x
3
+
□
x
2
+
□
x
+
□
7
)
(
x
−
a
)
(
x
−
b
)
(
x
−
c
)
=
x
3
−
□
x
2
+
□
x
−
□
7)\ (x-a)(x-b)(x-c)=x^3-\square x^2+\square x-\square
7
)
(
x
−
a
)
(
x
−
b
)
(
x
−
c
)
=
x
3
−
□
x
2
+
□
x
−
□
8
)
(
a
+
b
+
c
)
2
=
a
2
+
b
2
+
c
2
+
□
+
□
+
□
8)\ (a+b+c)^2=a^2+b^2+c^2+\square+\square+\square
8
)
(
a
+
b
+
c
)
2
=
a
2
+
b
2
+
c
2
+
□
+
□
+
□
9
)
(
a
b
+
b
c
+
c
a
)
2
=
a
2
b
2
+
b
2
c
2
+
c
2
a
2
+
□
9)\ (ab+bc+ca)^2=a^2b^2+b^2c^2+c^2a^2+\square
9
)
(
ab
+
b
c
+
c
a
)
2
=
a
2
b
2
+
b
2
c
2
+
c
2
a
2
+
□
10
)
(
a
+
b
)
3
=
a
3
+
□
+
□
+
b
3
10)\ (a+b)^3=a^3+\square+\square+b^3
10
)
(
a
+
b
)
3
=
a
3
+
□
+
□
+
b
3
11
)
(
a
−
b
)
3
=
a
3
−
□
+
□
−
b
3
11)\ (a-b)^3=a^3-\square+\square-b^3
11
)
(
a
−
b
)
3
=
a
3
−
□
+
□
−
b
3
12
)
(
a
2
+
a
b
+
b
2
)
(
a
2
−
a
b
+
b
2
)
=
□
+
□
+
□
12)\ (a^2+ab+b^2)(a^2-ab+b^2)=\square+\square+\square
12
)
(
a
2
+
ab
+
b
2
)
(
a
2
−
ab
+
b
2
)
=
□
+
□
+
□
13
)
(
x
2
+
x
+
1
)
(
x
2
−
x
+
1
)
=
□
+
□
+
1
13)\ (x^2+x+1)(x^2-x+1)=\square+\square+1
13
)
(
x
2
+
x
+
1
)
(
x
2
−
x
+
1
)
=
□
+
□
+
1
2. 인수분해 공식
1
)
a
2
+
2
a
b
+
b
2
=
(
□
+
□
)
2
1)\ a^2+2ab+b^2=(\square+\square)^2
1
)
a
2
+
2
ab
+
b
2
=
(
□
+
□
)
2
2
)
a
2
−
2
a
b
+
b
2
=
(
□
−
□
)
2
2)\ a^2-2ab+b^2=(\square-\square)^2
2
)
a
2
−
2
ab
+
b
2
=
(
□
−
□
)
2
3
)
x
2
+
(
a
+
b
)
x
+
a
b
=
(
□
+
□
)
(
□
+
□
)
3)\ x^2+(a+b)x+ab=(\square+\square)(\square+\square)
3
)
x
2
+
(
a
+
b
)
x
+
ab
=
(
□
+
□
)
(
□
+
□
)
4
)
a
c
x
2
+
(
a
d
+
b
c
)
x
+
b
d
=
(
□
+
□
)
(
□
+
□
)
4)\ acx^2+(ad+bc)x+bd=(\square+\square)(\square+\square)
4
)
a
c
x
2
+
(
a
d
+
b
c
)
x
+
b
d
=
(
□
+
□
)
(
□
+
□
)
5
)
a
2
−
b
2
=
(
□
−
□
)
(
□
+
□
)
5)\ a^2-b^2=(\square-\square)(\square+\square)
5
)
a
2
−
b
2
=
(
□
−
□
)
(
□
+
□
)
6
)
a
3
+
b
3
=
(
□
+
□
)
(
□
−
□
+
□
)
6)\ a^3+b^3=(\square+\square)(\square-\square+\square)
6
)
a
3
+
b
3
=
(
□
+
□
)
(
□
−
□
+
□
)
7
)
a
3
−
b
3
=
(
□
−
□
)
(
□
+
□
+
□
)
7)\ a^3-b^3=(\square-\square)(\square+\square+\square)
7
)
a
3
−
b
3
=
(
□
−
□
)
(
□
+
□
+
□
)
8
)
a
2
+
b
2
+
c
2
+
2
a
b
+
2
b
c
+
2
c
a
=
(
□
+
□
+
□
)
2
8)\ a^2+b^2+c^2+2ab+2bc+2ca=(\square+\square+\square)^2
8
)
a
2
+
b
2
+
c
2
+
2
ab
+
2
b
c
+
2
c
a
=
(
□
+
□
+
□
)
2
9
)
a
4
+
a
2
b
2
+
b
4
=
(
□
+
□
+
□
)
(
□
−
□
+
□
)
9)\ a^4+a^2b^2+b^4=(\square+\square+\square)(\square-\square+\square)
9
)
a
4
+
a
2
b
2
+
b
4
=
(
□
+
□
+
□
)
(
□
−
□
+
□
)
10
)
x
4
+
x
2
+
1
=
(
□
+
□
+
1
)
(
□
−
□
+
1
)
10)\ x^4+x^2+1=(\square+\square+1)(\square-\square+1)
10
)
x
4
+
x
2
+
1
=
(
□
+
□
+
1
)
(
□
−
□
+
1
)
11
)
a
3
+
b
3
+
c
3
−
3
a
b
c
=
(
□
+
□
+
□
)
(
□
+
□
+
□
−
□
−
□
−
□
)
11)\ a^3+b^3+c^3-3abc=(\square+\square+\square)(\square+\square+\square-\square-\square-\square)
11
)
a
3
+
b
3
+
c
3
−
3
ab
c
=
(
□
+
□
+
□
)
(
□
+
□
+
□
−
□
−
□
−
□
)
12
)
a
3
+
b
3
+
c
3
−
3
a
b
c
=
1
2
(
□
+
□
+
□
)
{
(
□
−
□
)
2
+
(
□
−
□
)
2
+
(
□
−
□
)
2
}
12)\ a^3+b^3+c^3-3abc=\frac{1}{2}(\square+\square+\square)\left\{(\square-\square)^2+(\square-\square)^2+(\square-\square)^2\right\}
12
)
a
3
+
b
3
+
c
3
−
3
ab
c
=
2
1
(
□
+
□
+
□
)
{
(
□
−
□
)
2
+
(
□
−
□
)
2
+
(
□
−
□
)
2
}
3. 변형공식
1
)
(
a
+
b
)
2
=
(
a
−
b
)
2
+
□
1)\ (a+b)^2=(a-b)^2+\square
1
)
(
a
+
b
)
2
=
(
a
−
b
)
2
+
□
2
)
(
a
−
b
)
2
=
(
a
+
b
)
2
−
□
2)\ (a-b)^2=(a+b)^2-\square
2
)
(
a
−
b
)
2
=
(
a
+
b
)
2
−
□
3
)
a
2
+
b
2
=
(
a
+
b
)
2
−
□
3)\ a^2+b^2=(a+b)^2-\square
3
)
a
2
+
b
2
=
(
a
+
b
)
2
−
□
4
)
a
2
+
b
2
=
(
a
−
b
)
2
+
□
4)\ a^2+b^2=(a-b)^2+\square
4
)
a
2
+
b
2
=
(
a
−
b
)
2
+
□
5
)
a
2
+
1
a
2
=
(
a
+
1
a
)
2
−
□
5)\ a^2+\frac{1}{a^2}=\left(a+\frac{1}{a}\right)^2-\square
5
)
a
2
+
a
2
1
=
(
a
+
a
1
)
2
−
□
6
)
a
2
+
1
a
2
=
(
a
−
1
a
)
2
+
□
6)\ a^2+\frac{1}{a^2}=\left(a-\frac{1}{a}\right)^2+\square
6
)
a
2
+
a
2
1
=
(
a
−
a
1
)
2
+
□
7
)
(
a
+
1
a
)
2
=
(
a
−
1
a
)
2
+
□
7)\ \left(a+\frac{1}{a}\right)^2=\left(a-\frac{1}{a}\right)^2+\square
7
)
(
a
+
a
1
)
2
=
(
a
−
a
1
)
2
+
□
8
)
a
3
+
b
3
=
(
a
+
b
)
3
−
□
8)\ a^3+b^3=(a+b)^3-\square
8
)
a
3
+
b
3
=
(
a
+
b
)
3
−
□
9
)
a
3
−
b
3
=
(
a
−
b
)
3
+
□
9)\ a^3-b^3=(a-b)^3+\square
9
)
a
3
−
b
3
=
(
a
−
b
)
3
+
□
10
)
a
3
+
1
a
3
=
(
a
+
1
a
)
3
−
□
10)\ a^3+\frac{1}{a^3}=\left(a+\frac{1}{a}\right)^3-\square
10
)
a
3
+
a
3
1
=
(
a
+
a
1
)
3
−
□
11
)
a
3
−
1
a
3
=
(
a
−
1
a
)
3
+
□
11)\ a^3-\frac{1}{a^3}=\left(a-\frac{1}{a}\right)^3+\square
11
)
a
3
−
a
3
1
=
(
a
−
a
1
)
3
+
□
12
)
a
2
+
b
2
+
c
2
+
a
b
+
b
c
+
c
a
=
1
2
{
□
+
□
+
□
}
12)\ a^2+b^2+c^2+ab+bc+ca=\frac{1}{2}\left\{\square+\square+\square\right\}
12
)
a
2
+
b
2
+
c
2
+
ab
+
b
c
+
c
a
=
2
1
{
□
+
□
+
□
}
13
)
a
2
+
b
2
+
c
2
−
a
b
−
b
c
−
c
a
=
1
2
{
□
+
□
+
□
}
13)\ a^2+b^2+c^2-ab-bc-ca=\frac{1}{2}\left\{\square+\square+\square\right\}
13
)
a
2
+
b
2
+
c
2
−
ab
−
b
c
−
c
a
=
2
1
{
□
+
□
+
□
}
14
)
a
2
+
b
2
+
c
2
=
(
a
+
b
+
c
)
2
−
□
14)\ a^2+b^2+c^2=(a+b+c)^2-\square
14
)
a
2
+
b
2
+
c
2
=
(
a
+
b
+
c
)
2
−
□
15
)
a
3
+
b
3
+
c
3
=
(
a
+
b
+
c
)
(
□
)
+
□
15)\ a^3+b^3+c^3=(a+b+c)(\square)+\square
15
)
a
3
+
b
3
+
c
3
=
(
a
+
b
+
c
)
(
□
)
+
□