viết thành hằng đẳng thức:(x+3)^2-9(y-3)^2
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài làm:
Ta có: \(\left\{4x-2\left(x-3\right)-3\left[x-3\left(4-2x\right)+8\right]\right\}.\left(-3x\right)\)
\(=\left[4x-2x+6-3\left(x-12+6x+8\right)\right].\left(-3x\right)\)
\(=\left(2x+6-3x+36-18x-24\right).\left(-3x\right)\)
\(=\left(-19x\right).\left(-3x\right)\)
\(=57x^2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bạn dùng định lý Ta - lét đảo trong tam giác là tính được.
Chúc bạn học tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài làm:
a) \(\left(a+b+c\right)^2+\left(a-b+c\right)^2+\left(a+b-c\right)^2+\left(b+c-a\right)^2\)
\(=4\left(a^2+b^2+c^2\right)+2\left(ab+bc+ca+ab-bc-ca+ca-bc-ab+bc-ab-ca\right)\)
\(=4\left(a^2+b^2+c^2\right)+2.0\)
\(=4\left(a^2+b^2+c^2\right)\)
b) \(\left(a+b+c\right)^2+a^2+b^2+c^2\)
\(=a^2+b^2+c^2+2\left(ab+bc+ca\right)+a^2+b^2+c^2\)
\(=\left(a^2+2ab+b^2\right)+\left(b^2+2bc+c^2\right)+\left(c^2+2ca+a^2\right)\)
\(=\left(a+b\right)^2+\left(b+c\right)^2+\left(c+a\right)^2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 3 : Ta có : \(A=\frac{2}{5}xy\left(x^2y-5x+10y\right)\)
\(A=\frac{2}{5}xy\cdot x^2y+\frac{2}{5}xy\left(-5x\right)+\frac{2}{5}xy\cdot10y\)
\(A=\frac{2}{5}x^3y^2-2x^2y+4xy^2\)
Chọn C
Bài 4 : \(\left(x-2\right)\left(x+5\right)=x\left(x+5\right)-2\left(x+5\right)\)
\(=x^2+5x-2x-10\)
\(=x^2+3x-10\)
Chọn B
Bài 3 :
Ta có: A = 2/5xy( x2y -5x + 10y )
= 2/5xy.x2y - 2/5xy.5x + 2/5xy.10y
= 2/5x3y2 - 2x2y + 4xy2.
Chọn đáp án C
Bài 4 :
Ta có ( x - 2 )( x + 5 )
= x( x + 5 ) - 2( x + 5 )
= x2 + 5x - 2x - 10 = x2 + 3x - 10.
Chọn đáp án B.
Hok tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=x\left(2x+3\right)-4\left(x+1\right)-2x\left(x-\frac{1}{2}\right)\)
\(=2x^2+3x-4x-4-2x^2+x\)
\(=\left(2x^2-2x^2\right)+\left(3x+x-4x\right)-4\)
\(=-4\)
\(\left(2x^3-3xy+12x\right)\left(-\frac{1}{6}xy\right)\)
\(=-\frac{2}{6}x^3.xy+\frac{3}{6}xy.xy-\frac{12}{6}x.xy\)
\(=-\frac{1}{3}x^4y+\frac{1}{2}x^2y^2-2x^2y\)
BÀi 1
Ta có A = x( 2x + 3 ) - 4( x + 1 ) - 2x( x - 1/2 ) = ( 2x.x + 3.x ) - ( 4.x + 4.1 ) - ( 2x.x - 1/2.2x )
= 2x2 + 3x - 4x - 4 - 2x2 + x
= - 4.
Chọn đáp án C
Bài 2
Ta có: ( 2x3 - 3xy + 12x )( - 1/6xy ) = ( - 1/6xy ).2x3 - 3xy( - 1/6xy ) + 12x( - 1/6xy )
= - 1/3x4y + 1/2x2y2 - 2x2y
Chọn đáp án D
Hok tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
323 =17.19.
Ta có: \(20^n+16^n-3^n-1=\left(20^n-3^n\right)+\left(16^n-1\right)\)
\(20^n-3^n⋮17,16^n-1⋮17\)(vì n chẵn)
\(\Rightarrow20^n+16^n-3^n-1⋮17\)(1)
Tương tự:
\(20^n+16^n-3^n-1=\left(20^n-1\right)+\left(16^n-3^n\right)\)
\(20^n-1⋮19,16^n-3^n⋮19\)(vì n chẵn)
\(\Rightarrow20^n+16^n-3^n-1⋮19\)(2)
Từ (1) và (2) \(\Rightarrow20^n+16^n-3^n-1⋮\left(17,19\right)=323\)(đpcm)
![](https://rs.olm.vn/images/avt/0.png?1311)
(3x - 4)(x - 2) = 3x(x - 9) - 3
=> 3x2 - 10x + 8 = 3x2 - 27x - 3
=> 27x - 10x = -3 - 8
=> 17x = -11
=> x = -11/17
\(\left(3x-4\right)\left(x-2\right)=3x\left(x-9\right)-3\)
\(\Leftrightarrow3x^2-6x-4x+8=3x^2-27x-3\)
\(\Leftrightarrow3x^2-10x+8=3x^2-27x-3\)
\(\Leftrightarrow17x+11=0\)
\(\Leftrightarrow17x=-11\)
\(\Leftrightarrow x=\frac{-11}{17}\)
Bài làm:
Ta có: \(\left(x+3\right)^2-9\left(y-3\right)^2\)
\(=\left(x+3\right)^2-\left[3\left(y-3\right)\right]^2\)
\(=\left[x+3-3\left(y-3\right)\right]\left[x+3+3\left(y-3\right)\right]\)
\(=\left(x+3-3y+9\right)\left(x+3+3y-9\right)\)
\(=\left(x-3y+12\right)\left(x+3y-6\right)\)
\(\left(x+3\right)^2-9\left(y-3\right)^2\)
\(=\left[x+3+3\left(x-3\right)\right].\left[x+3-3\left(x-3\right)\right]\)