Đề bài: Viết tích thành tổng ( theo hằng đẳng thức đáng nhớ)
1. ( x mũ 2 - y ) mũ 3
2. ( x - 2 + y ) mũ 3
3. ( z + y mũ 2 ) mũ 3
4. ( x - y + z ) mũ 3
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
17 tháng 8 2021
h, \(27x^3-8=\left(3x-2\right)\left(9x^2+6x+4\right)\)
\(\Rightarrow\left(27x^3-8\right):\left(3x-2\right)\\ =\left(3x-2\right)\left(9x^2+6x+4\right):\left(3x-2\right)\\ =9x^2+6x+4\)
g, \(x^4-2x^2+1=\left(x^2-1\right)^2\)
\(\Rightarrow\left(x^4-2x^2+1\right):\left(1-x^2\right)\\ =\left(x^2-1\right)^2:\left(1-x^2\right)\\ =x^2-1\)
6 tháng 8 2017
x^4-5x^2+4=x^4-x^2-(4x^2-4) = x^2(x^2-1)-4(x^2-1)
=(x^2-4)(x^2-1)
=(x-2)(x+2)(x-1)(x+1)
ND
26 tháng 5 2018
4. 4x2 + 4x + 1 = ( 2x + 1)2
5. \(\dfrac{1}{4}x-\dfrac{2}{3}xy+\dfrac{4}{9}y^2\) \(=\left(\dfrac{1}{2}x\right)^2-2.\dfrac{1}{2}x.\dfrac{2}{3}+\left(\dfrac{2}{3}y\right)^2\)
\(=\left(\dfrac{1}{2}x-\dfrac{2}{3}y\right)^2\)
6. \(4a^2-\dfrac{4}{3}ab+\dfrac{1}{9}b^2=\left(2a\right)^2-2.2a.\dfrac{1}{3}+\left(\dfrac{1}{3}b\right)^2=\left(2a-\dfrac{1}{3}b\right)^2\)
7.
\(9x^2+4xy+\dfrac{4}{9}y^2-25z^2=\left(3x+\dfrac{2}{3}y\right)^2-\left(5z\right)^2=\left(3x+\dfrac{2}{3}y-5z\right)\left(3x+\dfrac{2}{3}y+5z\right)\)
ND
26 tháng 5 2018
1. \(x^4-2x^2+1=\left(x^2-1\right)^2\)
2. \(x^2+5x+\dfrac{25}{4}=x^2+2.x.\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2=\left(x+\dfrac{5}{2}\right)^2\)
3. \(16x^2-8x+1=\left(4x-1\right)^2\)
4. \(x^2+x-y^2+y=\left(x-y\right)\left(x+y\right)+\left(x+y\right)=\left(x-y+1\right)\left(x+y\right)\)
5. \(\dfrac{1}{4}x^2-\dfrac{4}{9}y^2=\left(\dfrac{1}{2}x-\dfrac{2}{3}y\right)\left(\dfrac{1}{2}x+\dfrac{2}{3}y\right)\)
6. \(a^2-2ab+b^2-x^2=\left(a-b\right)^2-x^2=\left(a-b-x\right)\left(a-b+x\right)\)
7. \(4x^2-20x+25-y^2=\left(2x-5\right)^2-y^2=\left(2x-5-y\right)\left(2x-5+y\right)\)
Giải:
1) \(\left(x^2-y\right)^3\)
\(=x^6-3x^4y+4x^2y^2-y^3\)
Vậy ...
2) \(\left(x-2+y\right)^3\)
\(=\left(x-2\right)^3+3\left(x-2\right)^2y+3\left(x-2\right)y^2+y^3\)
\(=x^3-3x^2+16x-2^3+3\left(x^2-4x-4\right)y+3\left(x-2\right)y^2+y^3\)
\(=x^3-3x^2+16x-2^3+3x^2-12x-12y+3\left(xy^2-2y^2\right)+y^3\)
\(=x^3-3x^2+16x-2^3+3x^2-12x-12y+3xy^2-6y^2+y^3\)
\(=x^3+4x-8-12y+3xy^2-6y^2+y^3\)
Vậy ...
3) \(\left(z+y^2\right)^3\)
\(=z^3+3z^2y^2+3zy^4+y^6\)
Vậy ...
4) \(\left(x-y+z\right)^3\)
\(=\left(x-y\right)^3+3\left(x-y\right)^2z+3\left(x-y\right)z^2+z^3\)
\(=x^3-3x^2y+3xy^2-y^3+3\left(x^2-2xy+y^2\right)z+3\left(xz^2-yz^2\right)+z^3\)
\(=x^3-3x^2y+3xy^2-y^3+3x^2-6xy+3y^2z+3xz^2-3yz^2+z^3\)
\(=-3x^2y+3xy^2-y^3+4x^2-6xy+3y^2z+3xz^2-3yz^2+z^3\)
Vậy ...