Viết đa thức thành tích
a, 8y2-125
b,8z3+27
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21 tháng 8 2021
1) \(\left(3x+2\right)^2-4\\ =\left(3x+2\right)^2-2^2\\ =\left(3x+2-2\right)\left(3x+2+2\right)\\ =3x.\left(3x+4\right)\)
2) \(4x^2-25y^2=\left(2x\right)^2-\left(5y\right)^2=\left(2x-5y\right)\left(2x+5y\right)\)
3) \(4x^2-49=\left(2x\right)^2-7^2=\left(2x-7\right)\left(2x+7\right)\)
4) \(8z^3+27=\left(2z\right)^3+3^3=\left(2z+3\right)\left(4z^2+6z+9\right)\)
5) \(\dfrac{9}{25}x^4-\dfrac{1}{4}=\left(\dfrac{3}{5}x^2\right)^2-\left(\dfrac{1}{2}\right)^2=\left(\dfrac{3}{5}x^2-\dfrac{1}{2}\right)\left(\dfrac{3}{5}x^2+\dfrac{1}{2}\right)\)
6) \(x^{32}-1\\ =\left(x^{16}\right)^2-1^2\\ =\left(x^{16}-1\right)\left(x^{16}+1\right)\\ =\left(x^8-1\right)\left(x^8+1\right)\left(x^{16}+1\right)\\ =\left(x^4-1\right)\left(x^4+1\right)\left(x^8+1\right)\left(x^{16}+1\right)\\ =\left(x^2-1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\left(x^{16}+1\right)\\ =\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\left(x^{16}+1\right)\)
21 tháng 8 2021
1: \(\left(3x+2\right)^2-4=3x\left(3x+4\right)\)
2: \(4x^2-25y^2=\left(2x-5y\right)\left(2x+5y\right)\)
3: \(4x^2-49=\left(2x-7\right)\left(2x+7\right)\)
4: \(8z^3+27=\left(2z+3\right)\left(4z^2-6z+9\right)\)
5: \(\dfrac{9}{25}x^4-\dfrac{1}{4}=\left(\dfrac{3}{5}x^2-\dfrac{1}{2}\right)\left(\dfrac{3}{5}x^2+\dfrac{1}{2}\right)\)
19 tháng 7 2021
a) \(8x^3-\dfrac{1}{27}=\left(2x-\dfrac{1}{3}\right)\left(4x^2+\dfrac{2}{3}x+\dfrac{1}{9}\right)\)
b) \(\dfrac{1}{8}a^3-125b^6=\left(\dfrac{1}{2}a-5b^2\right)\left(\dfrac{1}{4}a+\dfrac{5}{2}ab^2+25b^4\right)\)
c) \(125+\left(a-b\right)^3=\left(5+a-b\right)\left(25-5a+5b+a^2-2ab+b^2\right)\)
20 tháng 7 2023
`a, 4x^2 - 25y^2 = (2x-5y)(2x+5y)`.
`b, 8x^3 +27 = (2x+3)(4x^2 - 6x + 9)`.
`c, 125x^3 - 64y^3 = (5x)^3 - (4y)^3 = (5x-4y)(25x^2 + 20xy + 16y^2)`.
GN
GV Nguyễn Trần Thành Đạt
Giáo viên
20 tháng 7 2023
\(a,\\ 4x^2-25y^2=\left(2x\right)^2-\left(5y\right)^2=\left(2x-5y\right)\left(2x+5y\right)\\ b,\\ 8x^3+27=\left(2x\right)^3+3^3=\left(2x+3\right)\left(4x^2+6x+9\right)\\ c,\\ 125x^3-64y^3=\left(5x\right)^3-\left(4y\right)^3=\left(5x-4y\right)\left(25x^2+20xy+16y^2\right)\)
T
27 tháng 10 2023
a, \(8^3yz+12^2yz+6xyz+yz\)
\(=512yz+144yz+6xyz+yz\)
\(=yz\left(512+14+6x+1\right)\)
\(=yz\left(527+6x\right)\)
$---$
b, \(81x^4\left(z^2-y^2\right)-z^2+y^2\)
\(=81x^4\left(z^2-y^2\right)-\left(z^2-y^2\right)\)
\(=\left(z^2-y^2\right)\left(81x^4-1\right)\)
\(=\left(z-y\right)\left(z+y\right)\left[\left(9x^2\right)^2-1^2\right]\)
\(=\left(z-y\right)\left(z+y\right)\left(9x^2-1\right)\left(9x^2+1\right)\)
\(=\left(z-y\right)\left(z+y\right)\left[\left(3x\right)^2-1^2\right]\left(9x^2+1\right)\)
\(=\left(z-y\right)\left(z+y\right)\left(3x-1\right)\left(3x+1\right)\left(9x^2+1\right)\)
$---$
c, \(\dfrac{x^3}{8}-\dfrac{y^3}{27}+\dfrac{x}{2}-\dfrac{y}{3}\)
\(=\left[\left(\dfrac{x}{2}\right)^3-\left(\dfrac{y}{3}\right)^3\right]+\left(\dfrac{x}{2}-\dfrac{y}{3}\right)\)
\(=\left(\dfrac{x}{2}-\dfrac{y}{3}\right)\left(\dfrac{x^2}{4}+\dfrac{xy}{6}+\dfrac{y^2}{9}\right)+\left(\dfrac{x}{2}-\dfrac{y}{3}\right)\)
\(=\left(\dfrac{x}{2}-\dfrac{y}{3}\right)\left(\dfrac{x^2}{4}+\dfrac{xy}{6}+\dfrac{y^2}{9}+1\right)\)
$---$
d, \(x^6+x^4+x^2y^2+y^4-y^6\)
\(=\left(x^6-y^6\right)+\left(x^4+x^2y^2+y^4\right)\)
\(=\left[\left(x^2\right)^3-\left(y^2\right)^3\right]+\left(x^4+x^2y^2+y^4\right)\)
\(=\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)+\left(x^4+x^2y^2+y^4\right)\)
\(=\left(x^4+x^2y^2+y^4\right)\left(x^2-y^2+1\right)\)
$Toru$
10 tháng 11 2019
\(27a^3-125b^3\)
\(=\left(3a\right)^3-\left(5b\right)^3\)
\(=\left(3a-5b\right)\left(9a^2+15ab+25b^2\right)\)
28 tháng 8 2021
Bài 1:
a: \(\left(3x+2\right)^2-4=3x\left(3x+4\right)\)
Bài 2:
a: \(4x^2+4x+1\)
b: \(9x^2+9x+\dfrac{9}{4}\)
LT
20 tháng 1 2021
Bạn viết lại đề được không!? Nếu đề có số âm thì bạn cần có thêm dấu ngoặc vào nhé!
TC
31 tháng 7 2021
1. ( 3x + 2)2 - 4
= (3x+2-2)(3x+2+2)
= 3x(3x+4)
2. 4x2 - 25y2
= (2x-5y)(2x+5y)
3. 4x2- 49
=(2x-7)(2x+7)
4. 8z3 + 27
=(2z+3)(4x2-6z+9)
5. \(\dfrac{9}{25}x^4-\dfrac{1}{4}\)
= \((\dfrac{3}{5}x^2-\dfrac{1}{2})(\dfrac{3}{5}x^2+\dfrac{1}{2})\)
6. x32 - 1
=(x16-1)(x16+1)
7. 4x2 + 4x + 1
=(2x+1)2
8. x2 - 20x + 100
=(x-10)2
9. y4 -14y2 + 49
=(y2-7)2
10. 125x3 - 64y3
= (5x-4y)(25x2+20xy+16y2)
31 tháng 7 2021
1) \(\left(3x+2\right)^2-4=\left(3x+2+2\right)\left(3x+2-2\right)=3x\left(3x+4\right)\)
2) \(4x^2-25y^2=\left(2x-5y\right)\left(2x+5y\right)\)
3) \(4x^2-49=\left(2x-7\right)\left(2x+7\right)\)
4) \(8z^3+27=\left(2z+3\right)\left(4z^2-6z+9\right)\)
5) \(\dfrac{9}{25}x^4-\dfrac{1}{4}=\left(\dfrac{3}{5}x^2-\dfrac{1}{2}\right)\left(\dfrac{3}{5}x^2+\dfrac{1}{2}\right)\)
6) \(x^{32}-1=\left(x^{16}-1\right)\left(x^{16}+1\right)\)
\(=\left(x^8-1\right)\left(x^8+1\right)\left(x^{16}+1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\left(x^{16}+1\right)\)
7) \(4x^2+4x+1=\left(2x+1\right)^2\)
8) \(x^2-20x+100=\left(x-10\right)^2\)
9) \(y^4-14y^2+49=\left(y^2-7\right)^2\)
TM
20 tháng 7 2023
a, \(25+10x+x^2=5^2+2.5x+x^2=\left(5+x\right)^2\)
b, \(8x^3-\dfrac{1}{8}=\left(2x\right)^3-\left(\dfrac{1}{2}\right)^3=\left(2x-\dfrac{1}{2}\right)\left[\left(2x\right)^2+2x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2\right]=\left(2x-\dfrac{1}{2}\right)\left(4x^2+x+\dfrac{1}{4}\right)\)
c, \(x^2-10x+25=x^2-2.5x+5^2=\left(x-5\right)^2\)
NV
20 tháng 7 2023
1. \(25+10x+x^2\\ \Leftrightarrow5^2+2\cdot5\cdot x+x^2\\ \Leftrightarrow\left(5+x\right)^2\\ \Leftrightarrow\left(5+x\right)\left(5+x\right)\)
2. \(8x^3-\dfrac{1}{8}\\ \Leftrightarrow\left(2x\right)^3-\left(\dfrac{1}{2}\right)^3\\ \Leftrightarrow\left(2x-\dfrac{1}{2}\right)\left[\left(2x\right)^2+2x\cdot\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2\right]\\ \Leftrightarrow\left(2x-\dfrac{1}{2}\right)\left[4x^2+x+\dfrac{1}{4}\right]\)
3. \(x^2-10x+25\\ \Leftrightarrow x^2-2\cdot5\cdot x+5^2\\ \Leftrightarrow\left(x-5\right)^2\\ \Leftrightarrow\left(x-5\right)\left(x-5\right)\)
Bạn sai đề rồi :
a ) \(8y^3-125\)
\(=\left(2y\right)^3-5^3\)
\(=\left(2y-5\right)\left(4y^2+2y.5+5^2\right)\)
\(=\left(2y-5\right)\left(4y^2+10y+25\right)\)
b) Ta thấy \(8z^3=\left(2z\right)^3\)còn \(27=3^3\)
Trở thành : \(\left(2z\right)^3+3^3\)
Rồi bạn bạn tự làm nha
Thanks