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\(a,\)\(100a^2+20a+1\)
\(=\left(10a\right)^2+2.10a.1+1^2\)
\(=\left(10a+1\right)^2\)
1: a) Ta có: \(A=x\left(x+2\right)+y\left(y-2\right)-2xy+37\)
\(=x^2+2x+y^2-2y-2xy+37\)
\(=\left(x^2-2xy+y^2\right)+\left(2x-2y\right)+37\)
\(=\left(x-y\right)^2+2\left(x-y\right)+37\)
\(=7^2+2.7+37\) (Vì \(x-y=7\))
\(=100\)
Vậy \(A=100\)
b) Ta có: \(B=x^2+4y^2-2x+10+4xy-4y\)
\(=\left(x^2+4xy+4y^2\right)-\left(2x+4y\right)+10\)
\(=\left(x+2y\right)^2-2\left(x+2y\right)+10\)
\(=5^2-2.5+10\)
\(=25\)
Vậy \(B=25\)
c) Ta có : \(C=\left(x-y\right)^2\)
\(=x^2-2xy+y^2\)
\(=\left(x^2+y^2\right)-2xy\)
\(=26-2.5\) (Vì \(x^2+y^2=26\) ; \(xy=5\))
\(=16\)
Vậy \(C=16\)
2: a) \(\left(x+y\right)^2-y^2=x^2+2xy+y^2-y^2\)
\(=x^2+2xy\)
\(=x\left(x+2y\right)\) \(\left(dpcm\right)\)
b) \(\left(x^2+y^2\right)^2-2xy^2=\left(x^2-2xy+y^2\right)\left(x^2+2xy+y^2\right)\)
\(=\left(x-y\right)^2\left(x+y\right)^2\) \(\left(dpcm\right)\)
c) \(\left(x+y\right)^2=x^2+2xy+y^2\)
\(=\left(x^2-2xy+y^2\right)+4xy\)
\(=\left(x-y\right)^2+4xy\) \(\left(dpcm\right)\)
Chúc bn học tốt ✔✔✔
A. \(y^2+6xy+9x^2=\left(y+3\right)^2\)
B. \(4x^2-12xy+9y^2=\left(2x-3y\right)^2\)
C. (x-2)(x+2)=(x)2-4
E. \(x^3+1=\left(x+1\right)\left(x^2-x+1\right)\)
F. \(x^3+9x^2+27x+27=\left(x+3\right)^3\)
Mình chịu câu D
Có gì sai thì sửa nhé
A.(x+2y).(x+2y-1) = x^2 +4xy + 4y^2 - x - 2y
B. (x-2y).(x+2y-1) = x^2 - x - 4y^2 + 2y
C. (x-2y).(x-2y+1) = x^2 - 4xy + 4y^2 + x - 2y
D.(x+2y).(x-2y) = x^2 - 4y^2
=>....
đề bài là : dùng hằng đẳng thức để khai triển và thu gọn các biểu thức
cau a : (3x^2y-6xy+9x)(-4/3xy)
=-4/3xy.3x^2y+4/3xy.6xy-4/3xy.9x
=-4x+8-8y
cau b : (1/3x+2y)(1/9x^2-2/3xy+4y^2)
=(1/3)^3-2/9x^2y+8y^3+4/3xy^2+2/9x^2y-4/3xy^2+8y^3
=(1/3)^3 + (2y)^3x-2
cau c : (x-2)(x^2-5x+1)+x(x^2+11)
=x^3-5x^2+x-2x^2+10x-2+x^3+11x
=2x^3-7x^2+22x-2
cau d := x^3 + 6xy^2 -27y^3
cau e := x^3 + 3x^2 -5x - 3x^2y - 9xy = 15y
cau f := x^2-2x+2x -4-2x-1
= x(x-2)-5
a)
\(5x(x-2y)+2(2y-x)^2=5x(x-2y)+2(x-2y)^2\)
\(=(x-2y)[5x+2(x-2y)]=(x-2y)(7x-4y)\)
b)
\(7x(y-4)^2-(4-y)^3=7x(y-4)^2+(y-4)^3=(y-4)^2(7x+y-4)\)
c)
\((4x-8)(x^2+6)-(4x-8)(x+7)+9(8-4x)\)
\(=(4x-8)(x^2+6)-(4x-8)(x+7)-9(4x-8)\)
\(=(4x-8)[(x^2+6)-(x+7)-9]=(4x-8)(x^2-x-10)=4(x-2)(x^2-x-10)\)
d)
\(x^2-xz-9y^2+3yz=(x^2-9y^2)-(xz-3yz)\)
\(=(x-3y)(x+3y)-z(x-3y)=(x-3y)(x+3y-z)\)
e)
\(x^2(x^2-6)-x^2+9=x^4-7x^2+9=(x^4-6x^2+9)-x^2\)
\(=(x^2-3)^2-x^2=(x^2-3-x)(x^2-3+x)\)
a)
\(5x(x-2y)+2(2y-x)^2=5x(x-2y)+2(x-2y)^2\)
\(=(x-2y)[5x+2(x-2y)]=(x-2y)(7x-4y)\)
b)
\(7x(y-4)^2-(4-y)^3=7x(y-4)^2+(y-4)^3=(y-4)^2(7x+y-4)\)
c)
\((4x-8)(x^2+6)-(4x-8)(x+7)+9(8-4x)\)
\(=(4x-8)(x^2+6)-(4x-8)(x+7)-9(4x-8)\)
\(=(4x-8)[(x^2+6)-(x+7)-9]=(4x-8)(x^2-x-10)=4(x-2)(x^2-x-10)\)
d)
\(x^2-xz-9y^2+3yz=(x^2-9y^2)-(xz-3yz)\)
\(=(x-3y)(x+3y)-z(x-3y)=(x-3y)(x+3y-z)\)
e)
\(x^2(x^2-6)-x^2+9=x^4-7x^2+9=(x^4-6x^2+9)-x^2\)
\(=(x^2-3)^2-x^2=(x^2-3-x)(x^2-3+x)\)
a) x2 + 4xy + 2y = ( x + 2y ) 2
b) 9x2 - 24xy + 16y2 = ( 3x - 4y ) 2