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Bài 7
Ta có:
VT = a³ + b³ = (a + b)(a² - ab + b²)
= (a + b)(a² - 2ab + b² + ab)
= (a + b)[(a - b)² + ab]
= VP
Vậy a³ + b³ = (a + b)[(a - b)² + ab]
Bài 8
(x + 2)³ + (x - 2)³ + x³ - 3x(x + 2)(x - 2)
= x³ + 6x² + 12x + 8 + x³ - 6x² + 12x - 8 + x³ - 3x(x² - 4)
= 3x³ + 24x - 3x³ + 12x
= 36x
![](https://rs.olm.vn/images/avt/0.png?1311)
22:
A=9x^2+12x+4+4x^2-28x+49-2(6x^2+15x+4x+10)
=13x^2-16x+53-12x^2-38x-20
=x^2-54x+33
=(-19)^2-54*(-19)+33=1420
Bài 4 :
\(A=5\left(x+3\right)\left(x-3\right)+\left(2x+3\right)^2+\left(x-6\right)^2\)
\(A=5\left(x^2-9\right)+\left(4x^2+12x+9\right)+\left(x^2-12x+36\right)\)
\(A=5x^2-45+4x^2+12x+9+x^2-12x+36\)
\(A=10x^2\)
Với x = -1/5 => A = \(10.\left(\dfrac{-1}{5}\right)^2=\dfrac{2}{5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 3:
1) \(x^2-25=x^2-5^2=\left(x+5\right)\left(x-5\right)\)
2) \(9x^2-\dfrac{1}{16}y^2=\left(3x\right)^2-\left(\dfrac{1}{4}y\right)^2=\left(3x+\dfrac{1}{4}y\right)\left(3x-\dfrac{1}{4}y\right)\)
3) \(x^6-y^4=\left(x^3\right)^2-\left(y^2\right)^2=\left(x^3+y^2\right)\left(x^3-y^2\right)\)
4) \(\left(2x-5\right)^2-64=\left(2x-5\right)^2-8^2=\left[\left(2x-5\right)+8\right]\left[\left(2x-5\right)-8\right]=\left(2x+3\right)\left(2x-13\right)\)
5) \(81-\left(3x+2\right)^2=9^2-\left(3x+2\right)=\left[9-\left(3x+2\right)\right]\left[9+\left(3x+2\right)\right]=\left(7-3x\right)\left(11+3x\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
17:x^2-9=(x-3)(x+3)
18: 4x^2-25=(2x-5)(2x+5)
19: =(x^2-y^2)(x^2+y^2)
=(x-y)(x+y)(x^2+y^2)
20: 9x^2+6xy+y^2=(3x+y)^2
21 6x-9-x^2
=-(x^2-6x+9)
=-(x-3)^2
22: x^2+4xy+4y^2
=x^2+2*x*2y+(2y)^2
=(x+2y)^2
23: =(x+y+x-y)(x+y-x+y)
=2x*2y=4xy
25: =(3x+1+x+1)(3x+1-x-1)
=(4x+2)*2x
=4x(2x+1)
27: =(2x-y)(4x^2+2xy+y^2)-6xy(2x-y)
=(2x-y)(2x-y)^2
=(2x-y)^3
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
5
\(=4^2-x^2=\left(4-x\right)\left(4+x\right)\)
6
\(=4^2-\left(3x+1\right)^2=\left(4-3x-1\right)\left(4+3x+1\right)=\left(3-3x\right)\left(5+3x\right)\\ =3\left(1-x\right)\left(5+3x\right)\)
7
\(=\left(2x+5\right)^2-\left(3x\right)^2=\left(2x+5+3x\right)\left(2x+5-3x\right)\\ =\left(5x+5\right)\left(5-x\right)\\ =5\left(x+1\right)\left(5-x\right)\)
8
\(=\left(2x-1-3x+1\right)\left(2x-1+3x-1\right)=\left(-x\right)\left(5x-2\right)\)
9
\(=\left(2x\right)^2-2.2x.y+y^2=\left(2x-y\right)^2\)
10
\(=\left(x+1\right)^2-\left(3y\right)^2=\left(x+1-3y\right)\left(x+1+3y\right)\)
11
\(=\left(x^2y^2\right)^2+2.2x^2y^2+2^2=\left(x^2y^2+2\right)\)
12
\(=\left(y-2\right)^2-x^2=\left(y-2-x\right)\left(y-2+x\right)\)
13
\(=1-\left(3\sqrt{3}x\right)^3=\left(1-3\sqrt{3}x\right)\left[1^2+3\sqrt{3}.x+\left(3\sqrt{3}.x\right)^2\right]=\left(1-3\sqrt{3}x\right)\left(1+3\sqrt{3}x+27x^2\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 5:
a) \(M=\left(2x-1\right)^2+2\left(2x-1\right)\left(3x+1\right)+\left(3x+1\right)^2\)
\(M=\left[\left(2x-1\right)+\left(3x+1\right)\right]^2\)
\(M=\left(5x\right)^2\)
Thay \(x=-\dfrac{1}{5}\) vào biểu thức M ta có:
\(\left(5\cdot-\dfrac{1}{5}\right)^2=\left(-1\right)^2=1\)
Vậy: ...
b) \(N=\left(3x-1\right)^2-2\left(9x^2-1\right)+\left(3x+1\right)^2\)
\(N=\left(3x-1\right)^2-2\left(3x+1\right)\left(3x-1\right)+\left(3x+1\right)^2\)
\(N=\left[\left(3x-1\right)-\left(3x+1\right)\right]^2\)
\(N=\left(-2\right)^2=4\)
Vậy: ...
Câu 11:
Thay \(x=-1,y=0,5\) vào biểu thức ta được:
\(\left(-1\right)^3\cdot0,5-14\cdot0,5^3-6\cdot\left(-1\right)\cdot0,5^2+0,5+2\approx7,1\)
(Không có đáp án phù hợp)
Câu 12:
Diện tích của hình tam giác là: \(\dfrac{1}{2}\cdot x\cdot y=\dfrac{1}{2}\cdot3\cdot5=7,5\left(cm^2\right)\)
Diện tích của hình vuông nhỏ là: \(x^2=3^2=9\left(cm^2\right)\)
Diện tích hình vuông lớn là: \(y^2=5^2=25\left(cm^2\right)\)
Tổng diện tích là: \(7,5+9+25=41,5\left(cm^2\right)\)
→ Chọn A