(a+b+c)2=(a+b)2+2(a+b)c+c2
=a2+2ab+b2+2ac+2bc+c2
(a+b-c)2=(a+b)2-2(a+b)c+c2
=a2+2ab+b2-2ab-2bc+c2
(a-b-c)2=(a-b)2-2(a-b)c+c2
=a2-2ab+b2-2ac+2bc+c2
khai triển các biểu thức sau:
\(a.\left(2x+3y\right)^2\)
\(b.2\left(\dfrac{1}{2}x^2+y\right)\left(x^2-2y\right)\)
\(c.\left(x+y+z\right)^2\)
BT1: Khai triển
\(a,\left(\dfrac{x^2}{2}+y^2\right)^2\)
\(b,\left(\dfrac{4}{5}x^2-\dfrac{2}{3}y\right)^2\)
\(c,\left(2x+\dfrac{1}{2}\right)\left(2x-\dfrac{1}{2}\right)\)
Khai triển hằng dẳng thức
1, \(\left(a+b-c\right)^2\)
2, \(\left(a-b+c\right)^2\)
3, \(\left(x-y+z\right).\left(x-y-z\right)\)
Bài 1 : Dùng hằng đẳng thức để khai triển và thu gọn các biểu thức sau
a) \(\left(-4xy-5\right).\left(5-4xy\right)\)
b) \(\left(a^2b+ab^2\right).\left(ab^2-a^2b\right)\)
c) \(\left(3x-4\right)^2+2.\left(3x-4\right).\left(4-x\right)+\left(4-x\right)^2\)
d) \(\left(a^2+ab+b^2\right).\left(a^2-ab+b^2\right)-\left(a^4+b^4\right)\)
65. Phân tích đa thức thành nhân tử
a) \(ab\left(a+b\right)-bc\left(b+c\right)+ac\left(a-c\right)\)
b) \(a\left(b^2+c^2\right)+b\left(c^2+a^2\right)+c\left(a^2+b^2\right)+2abc\)
c) \(\left(a+b\right)\left(a^2-b^2\right)+\left(b+c\right)\left(b^2+c^2\right)+\left(c+a\right)\left(c^2+a^2\right)\)
d) \(a^3\left(b-c\right)+b^3\left(c-a\right)+c^3\left(a-b\right)\)
e) \(a^3\left(c-b^2\right)+b^3\left(a-c^2\right)+c^3\left(b-a^2\right)+abc\left(abc-1\right)\)
65. Phân tích đa thức thành nhân tử
a) \(ab\left(a+b\right)-bc\left(b+c\right)+ac\left(a-c\right)\)
b) \(a\left(b^2+c^2\right)+b\left(c^2+a^2\right)+c\left(a^2+b^2\right)+2abc\)
c) \(\left(a+b\right)\left(a^2-b^2\right)+\left(b+c\right)\left(b^2-c^2\right)+\left(c+a\right)\left(c^2-a^2\right)\)
d) \(a^3\left(b-c\right)+b^3\left(c-a\right)+c^3\left(a-b\right)\)
e) \(a^3\left(c-b^2\right)+b^3\left(a-c^2\right)+c^3\left(b-a^2\right)+abc\left(abc-1\right)\)
PTĐT thành nhân tử
a) \(A=a\left(b+c-a\right)^2+b\left(c+a-b\right)^2+c\left(a+b-c\right)^2+\left(a+b-c\right)\left(b+c-a\right)\left(c+a-b\right)\)
b) \(B=\left(a+b-c\right)^3+\left(a-b+c\right)^3+\left(-a+b+c\right)^3-\left(a+b+c\right)^3\)
c) \(C=bc\left(a+b\right)\left(b-c\right)-ac\left(b+d\right)\left(a-c\right)+ab\left(c+d\right)\left(c-b\right)\)
66. Phân tích đa thức thành nhân tử:
a) \(a\left(b+c\right)^2\left(b-c\right)+b\left(c+a\right)^2\left(c-a\right)+c\left(a+b\right)^2\left(a-b\right)\)
b) \(a\left(b-c\right)^3+b\left(c-a\right)^3+c\left(a-b\right)^3\)
c) \(a^2b^2\left(a-b\right)+b^2c^2\left(b-c\right)+c^2a^2\left(c-a\right)\)
d) \(a\left(b^2+c^2\right)+b\left(c^2+a^2\right)+c\left(a^2+b^2\right)-2abc-a^3-b^3-c^3\)
e) \(a^4\left(b-c\right)+b^4\left(c-a\right)+c^4\left(a-b\right)\)
Phân tích đa thức thành nhân tử :
a) \(â\left(b+c\right)^2\left(b-c\right)+b\left(c+a\right)^2\left(c-a\right)+c\left(a+b\right)^2\left(a-b\right)\)
b) \(a\left(b-c\right)^3+b\left(c-a\right)^3+c\left(a-b\right)^3\)
c) \(a^2b^2\left(a-b\right)+b^2c^2\left(b-c\right)+c^2a^2\left(c-a\right)\)
d) \(a\left(b^2+c^2\right)+b\left(c^2+a^2\right)+c\left(a^2+b^2\right)-2abc-a^3-b^3-c^3\)
e) \(a^4\left(b-c\right)+b^4\left(c-a\right)+c^4\left(a-b\right)\)
