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Trả lời:
7, 5( x + y )2 + 15( x + y )
= 5( x + y )( x + y + 3 )
9, 7x( y - 4 )2 - ( 4 - y )3
= 7x ( 4 - y )2 - ( 4 - y )
= ( 4 - y )2 ( 7x - 4 + y )
11, ( x + 1 )( y - 2 ) - ( 2 - y )2
= ( x + 1 )( y - 2 ) - ( y - 2 )2
= ( y - 2 )( x + 1 - y + 2 )
= ( y - 2 )( x - y + 3 )
8, 9x ( x - y ) - 10 ( y - x )2
= 9x ( x - y ) - 10 ( x - y )2
= ( x - y )[ ( 9x - 10 ( x - y ) ]
= ( x - y )( 9x - 10x + 10y )
= ( x - y )( 10y - x )
10, ( a - b )2 - ( a + b )( b - a )
= ( b - a )2 - ( a + b )( b - a )
= ( b - a )( b - a - a - b )
= - 2a( b - a )
= 2a ( a - b )
12, 2x ( x - 3 ) + y ( x - 3 ) + ( 3 - x )
= 2x ( x - 3 ) + y ( x - 3 ) - ( x - 3 )
= ( x - 3 )( 2x + y - 1 )
Câu c phải là \(\left(\frac{x}{2}-y\right)^3\) chứ không phải \(\left(\frac{4}{2}-2\right)^3\)
a) \(\dfrac{10^{12}+5^{11}.2^9-5^{13}.2^8}{4.5^5.10^6}\)
\(=\dfrac{2^{12}.5^{12}+5^{11}.2^9-5^{13}.2^8}{2^2.5^5.2^6.5^6}\)
\(=\dfrac{2^{12}.5^{12}+5^{11}.2^9-5^{13}.2^8}{2^8.5^{11}}\)
\(=\dfrac{\left(2^8.5^{11}\right)\left(2^4.5+2-5^2\right)}{2^8.5^{11}}\)
\(=2^4.5+2-5^2\)
\(=57\)
b) \(\dfrac{\left[5\left(x-y\right)^4-3\left(x-y\right)^3+4\left(x-y\right)^2\right]}{\left(y-x\right)^2}\)
\(=\dfrac{\left(x-y\right)^2\left[5\left(x-y\right)^2-3\left(x-y\right)+4\right]}{\left(y-x\right)^2}\)
\(=\dfrac{\left(x^2+y^2-2xy\right)\left[5\left(x-y\right)^2-3\left(x-y\right)+4\right]}{\left(y^2+x^2-2xy\right)}\)
\(=5\left(x-y\right)^2-3\left(x-y\right)+4\)
c) \(\dfrac{\left(x+y\right)^5-2\left(x+y\right)^4+3\left(x+y\right)^3}{-5\left(x+y\right)^3}\)
\(=\dfrac{\left(x+y\right)^3\left[5\left(x+y\right)^2-2\left(x+y\right)+3\right]}{-5\left(x+y\right)^3}\)
\(=\dfrac{5\left(x+y\right)^2-2\left(x+y\right)+3}{-5}\)
\(B=\left(x+y\right)^3+3\left(x-y\right)\left(x+y\right)^2+3\left(x-y\right)^2\left(x+y\right)+\left(x-y\right)^3\)
\(=\left(x+y\right)^3+3\cdot\left(x+y\right)^2\cdot\left(x-y\right)+3\cdot\left(x+y\right)\cdot\left(x-y\right)^2+\left(x-y\right)^3\)
\(=\left[\left(x+y\right)+\left(x-y\right)\right]^3\)
\(=\left(x+y+x-y\right)^3\)
\(=\left(2x\right)^3\)
\(=8x^3\)
\(---\)
\(C=8\left(x+2y\right)^3-6\left(x+2y\right)^2x+12\left(x+2y\right)x^2-8x^3\) (sửa đề)
\(=\left[2\left(x+2y\right)\right]^3-3\cdot\left(x+2y\right)^2\cdot2x+3\cdot\left(x+2y\right)\cdot\left(2x\right)^2-\left(2x\right)^3\)
\(=\left[2\left(x+2y\right)-2x\right]^3\)
\(=\left(2x+4y-2x\right)^3\)
\(=\left(4y\right)^3\)
\(=64y^3\)
\(---\)
\(D=\left(x-y\right)^3-3\cdot\dfrac{\left(x-y\right)^2}{2}\cdot y+3\cdot\dfrac{\left(x-y\right)}{4}\cdot y^2-\dfrac{y^3}{8}\)
\(=\left(x-y\right)^3-3\cdot\left(x-y\right)^2\cdot\dfrac{y}{2}+3\cdot\left(x-y\right)\cdot\left(\dfrac{y}{2}\right)^2-\left(\dfrac{y}{2}\right)^3\)
\(=\left[\left(x-y\right)-\dfrac{y}{2}\right]^3\)
\(=\left(x-y-\dfrac{y}{2}\right)^3\)
\(=\left(x-\dfrac{3}{2}y\right)^3\)
#\(Toru\)
a. x4 + x2y2 + y4 = (x4 + 2x2y2 + y4) - x2y2
= (x2 + y2)2 – (xy)2
= [(x2 + y2) + xy] [(x2 + y2) – xy]
= (x2 + xy + y2)(x2 –xy + y2)
\(\left(x-1\right)^3-\left(x+1\right)^3+6\left(x+1\right)\left(x-1\right)\)
\(=-2\left(x^2-2x+1+x^2-1+x^2+2x+1\right)+6\left(x^2-1\right)\)
\(=-2\left(3x^2+1\right)+6x^2-6\)
\(=-6x^2-2+6x^2-6\)
\(=-8\)
Vậy giá trị của của biểu thức không phụ thuộc vào biến x.
\(a)4{{\rm{x}}^2} - 12{\rm{x}}y + 9{y^2} = {\left( {2{\rm{x}}} \right)^2} - 2.2{\rm{x}}.3y + {\left( {3y} \right)^2} = {\left( {2{\rm{x}} - 3y} \right)^2}\)
\(b){x^3} + 9{{\rm{x}}^2} + 27{\rm{x}} + 27 = {x^3} + 3.{x^2}.3 + 3.x{.3^2} + {3^3} = {\left( {x + 3} \right)^3}\)
\(c)8{y^3} - 12{y^2} + 6y - 1 = {\left( {2y} \right)^3} - 3.{\left( {2y} \right)^2}.1 + 3.2y{.1^2} - {1^3} = {\left( {2y - 1} \right)^3}\)
\(\begin{array}{l}d) {\left( {2{\rm{x}} + y} \right)^2} - 4{y^2}\\ = {\left( {2{\rm{x}} + y} \right)^2} - {\left( {2y} \right)^2}\\ = \left( {2{\rm{x}} + y + 2y} \right)\left( {2{\rm{x}} + y - 2y} \right) = \left( {2{\rm{x}} + 3y} \right)\left( {2{\rm{x}} - y} \right)\end{array}\)
\(e) 27{y^3} + 8 = {\left( {3y} \right)^3} + {2^3} = \left( {3y + 2} \right)\left( {9{y^2} - 6y + 4} \right)\)
\(g) 64 - 125{{\rm{x}}^3} = {4^3} - {\left( {5{\rm{x}}} \right)^3} = \left( {4 - 5{\rm{x}}} \right)\left( {16 + 20{\rm{x}} + 25{{\rm{x}}^2}} \right)\)
( - 12 x 4 y + 4 x 3 – 8 x 2 y 2 ) : ( - 4 x ) 2 = ( - 12 x 4 y ) : ( - 4 x 2 ) + ( 4 x 3 ) : ( - 4 x 2 ) – ( 8 x 2 y 2 ) : ( - 4 x 2 ) = 3 x 2 y – x + 2 y 2
Đáp án cần chọn là: D