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9) \(\left(a+b\right)^3-\left(a-b\right)^3\)
\(=\left(a+b-a+b\right)\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)
\(=b^2\left[a^2+2ab+b^2+a\left(a-b\right)+b\left(a-b\right)+a^2-2ab+b^2\right]\)
\(=b^2\left(a^2+2ab+b^2+a^2-ab+ab-b^2+a^2-2ab+b^2\right)\)
\(=b^2\left(3a^2+b^2\right)\)
10) \(\left(6x-1\right)^2-\left(3x+2\right)^2\)
\(=\left(6x-1-3x-2\right)\left(6x-1+3x+2\right)\)
\(=\left(3x-3\right)\left(9x+1\right)\)
11) \(x^2-4x^2y^2+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-4x^2y^2\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y-2xy\right)\left(x+y+2xy\right)\)
12) \(\left(x^2-25\right)^2-\left(x-5\right)^2\)
\(=\left(x^2-25-x+5\right)\left(x^2-25+x-5\right)\)
\(=\left(x^2-x-20\right)\left(x^2-30+x\right)\)
13) \(x^6-x^4+2x^3+2x^2\)
\(=x^6-x^4+2x^3+2x^2-1+1\)
\(=\left(x^6+2x^3+1\right)-\left(x^4-2x^2+1\right)\)
\(=\left[\left(x^3\right)^2+2x^3.1+1^2\right]-\left[\left(x^2\right)^2-2x^2.1+1^2\right]\)
\(=\left(x^3+1\right)^2-\left(x^2-1\right)^2\)
\(=\left(x^3+1-x^2+1\right)\left(x^3+1+x^2-1\right)\)
\(=\left(x^3-x^2+2\right)\left(x^3+x^2\right)\)
1) \(\left(x+y\right)^2-25\)
\(=\left(x+y\right)^2-5^2\)
\(=\left(x+y-5\right)\left(x+y+5\right)\)
2) \(100-\left(3x-y\right)^2\)
\(=10^2-\left(3x-y\right)^2\)
\(=\left(10-3x+y\right)\left(10+3x-y\right)\)
3) \(64x^2-\left(8a+b\right)^2\)
\(=\left(8x\right)^2-\left(8a+b\right)^2\)
\(=\left(8x-8a-b\right)\left(8x+8a+b\right)\)
4) \(4a^2b^4-c^4d^2\)
\(=\left(2ab^2\right)^2-\left(c^2d\right)^2\)
\(=\left(2ab^2-c^2d\right)\left(2ab^2+c^2d\right)\)
5) Đề đúng ko vậy ạ?
6) \(16x^3+54y^3\)
\(=2\left(8x^3+27y^3\right)\)
\(=2\left[\left(2x\right)^3+\left(3y\right)^3\right]\)
\(=2\left(2x+3y\right)\left[\left(2x\right)^2-2x.3y+\left(3y\right)^2\right]\)
\(=2\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)\)
7) \(8x^3-y^3\)
\(=\left(2x\right)^3-y^3\)
\(=\left(2x-y\right)\left[\left(2x\right)^2+2xy+y^2\right]\)
\(=\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
8) \(\left(a+b\right)^2-\left(2ab-b\right)^2\)
\(=\left(a+b-2ab+b\right)\left(a+b+2ab-b\right)\)
\(=\left(a+2b-2ab\right)\left(a+2ab\right)\)
Đưa về hằng đẳng thức :
c) \(\)Câu này đề sai nhé:
Phải là: \(\left(x+3\right).\left(x^2-3x+9\right)\) hoặc \(\left(x-3\right).\left(x^2+3x+9\right)\) thì mới ra được hằng đẳng thức nhé.
d) \(x^2-x-\frac{1}{4}\)
\(=-\left(x^2+x+\frac{1}{4}\right)\)
\(=-\left[x^2+2.x.\frac{1}{2}+\left(\frac{1}{2}\right)^2\right]\)
\(=-\left(x+\frac{1}{2}\right)^2.\)
Chúc bạn học tốt!
Bài 1:
- a,(2+xy)^2=4+4xy+x^2y^2
- b,(5-3x)^2=25-30x+9x^2
- d,(5x-1)^3=125x^3 - 75x^2 + 15x^2 - 1
Áp dụng công thức : (A + B)3 = A3 + 3A2B + 3AB2 + B3
(A - B)3 = A3 - 3A2B + 3AB2 -B3
a) (3x + 1)3 = (3x)3 + 3.(3x)2.1 + 3.3x.1 + 13 = 27x3 + 27x2 + 9x + 1
b) \(\left(\frac{x}{3}-1\right)^3=\left(\frac{x}{3}\right)^3-3\cdot\left(\frac{x}{3}\right)^2\cdot1+3\cdot\left(\frac{x}{3}\right)\cdot1^2-1^3\)
\(=\frac{x^3}{27}-3\cdot\frac{x^2}{9}\cdot1+3\cdot\frac{x}{3}\cdot1-1\)
= \(\frac{x^3}{27}-\frac{x^2}{3}+x-1\)
c) \(\left(2x-\frac{1}{x}\right)^3=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot\frac{1}{x}+3\cdot2x\cdot\left(\frac{1}{x}\right)^2-\left(\frac{1}{x}\right)^3\)
\(=8x^3-3\cdot4x^2\cdot\frac{1}{x}+6x\cdot\frac{1}{x^2}-\frac{1}{x^3}\)
\(=8x^3-12x+\frac{6}{x}-\frac{1}{x^3}\)
d) \(\left(-y^2+3x\right)^3=\left(3x-y^2\right)^3=\left(3x\right)^3-3\cdot\left(3x\right)^2\cdot y^2+3\cdot3x\cdot y^4-y^6\)
= 27x3 - 27x2y2 + 9xy4 - y6
= -y6 + 9xy4 - 27x2y2 + 27x3
Tương tự câu cuối :>
a) \(A=\left(3x-2\right)\left(3x+2\right)-\left(3x+1\right)^2-3.\left(-2x-1\right)\)
\(=\left(3x\right)^2-4-\left(9x^2+6x+1\right)+6x+3\)
\(=9x^2-4-9x^2-6x-1+6x+3\)
\(=-2\) không phụ thuộc vào x
b) \(B=\left(x+1\right)\left(x-1\right)-\left(x-2\right)^2-4.\left(x+3\right)\)
\(=x^2-1-\left(x^2-4x+4\right)-\left(4x+12\right)\)
\(=x^2-1-x^2+4x-4-4x-12\)
\(=-17\)không phụ thuộc vào x.
a)8x3 + * + * + 27y3 = (* + *)3
=>A=(2x+3y)^3
b) (2x+1)^3
c)(x-2y)^3
d)(3x-2)(3x+2)
e)(3x-1)(9x^2+3x+1)
f)....................
6: \(27x^3+1=\left(3x+1\right)\left(9x^2-3x+1\right)\)
7: \(\left(2x+1\right)^2=4x^2+4x+1\)
8: \(\left(2x-1\right)^2=4x^2-4x+1\)
9: \(9-16x^2=\left(3-4x\right)\left(3+4x\right)\)