Bài 1:

a) \(2x\left( {x - 7x - 3} \right)\) \( = 2x\left( { - 6x - 3} \right) = - 12{x^2} - 6x\).

b) \(\left( { - 2x + y - 7xy} \right).4xy\) \( = - 8{x^2}y + 4x{y^2} - 28{x^2}{y^2}\)

c) \(\left( { - 5x} \right)\left( {2{x^2} + 3x - 5} \right)\)\( = - 10{x^3} - 15{x^2} + 25x\).

e) \(\left( {x - 2x + 3} \right)\left( {x - 4} \right) = \left( { - x + 3} \right)\left( {x - 4} \right)\)

\( =  - {x^2} + 4x + 3x - 12 =  - {x^2} + 7x - 12\)

g) \(\left( {25x + 10xy + 4y} \right)\left( {5x - 2y} \right)\)

\(\begin{array}{l} = 125{x^2} - 50xy + 50{x^2}y - 20x{y^2} + 20xy - 8{y^2}\\ = 125{x^2} - 30xy + 50{x^2}y - 20x{y^2} - 8{y^2}\end{array}\)

Bài 2:

d) \(\left( {2x - xy + y} \right)\left( { - 3x} \right) = - 6{x^2} + 3{x^2}y - 3xy\)

e) \(\left( {2x - 3x - 1} \right)\left( {5x + 2} \right) = \left( { - x - 1} \right)\left( {5x + 2} \right)\)

\( =  - 5{x^2} - 2x - 5x - 2 =  - 5{x^2} - 7x - 2\)

h) \(\left( {5x - {x^2} + 2x - 3} \right)\left( {4x - x + 2} \right) = \left( { - {x^2} + 7x - 3} \right)\left( {3x + 2} \right)\)

\(\begin{array}{l} =  - 3{x^3} - 2{x^2} + 21{x^2} + 14x - 9x - 6\\ =  - 3{x^3} + 19{x^2} + 5x - 6\end{array}\)

h) \(\left( {x + 4} \right)\left( {{x^2} - 4x + 16} \right) = {x^3} + {4^3} = {x^3} + 64\)h) \(\left( {x - 3y} \right)\left( {{x^2} + 3xy + 9{y^2}} \right) = {x^3} - {\left( {3y} \right)^3} = {x^3} - 27{y^3}\).

1) \(\left( {x - 1} \right)\left( {x + 3} \right) = {x^2} + 3x - x - 3 = {x^2} + 2x - 3\).

Bài 3:

a) \(2004 - 16 = 2004 - 4 - 12 = 2000 - 12 = 1988\)

b) \(10,2.9,8 - 9,8.0,2 + 10,22 - 10,2.0,2\)

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Đáp án:

Giải thích các bước giải::

a) 2x(x−7x−3)2x(x−7x−3) =2x(−6x−3)=−12x2−6x=2x(−6x−3)=−12x2−6x.

b) (−2x+y−7xy).4xy(−2x+y−7xy).4xy =−8x2y+4xy2−28x2y2=−8x2y+4xy2−28x2y2

c) (−5x)(2x2+3x−5)(−5x)(2x2+3x−5)=−10x3−15x2+25x=−10x3−15x2+25x.

e) (x−2x+3)(x−4)=(−x+3)(x−4)(x−2x+3)(x−4)=(−x+3)(x−4)

=−x2+4x+3x−12=−x2+7x−12=−x2+4x+3x−12=−x2+7x−12

g) (25x+10xy+4y)(5x−2y)(25x+10xy+4y)(5x−2y)

=125x2−50xy+50x2y−20xy2+20xy−8y2=125x2−30xy+50x2y−20xy2−8y2=125x2−50xy+50x2y−20xy2+20xy−8y2=125x2−30xy+50x2y−20xy2−8y2

Bài 2:

d) (2x−xy+y)(−3x)=−6x2+3x2y−3xy(2x−xy+y)(−3x)=−6x2+3x2y−3xy

e) (2x−3x−1)(5x+2)=(−x−1)(5x+2)(2x−3x−1)(5x+2)=(−x−1)(5x+2)

=−5x2−2x−5x−2=−5x2−7x−2=−5x2−2x−5x−2=−5x2−7x−2

h) (5x−x2+2x−3)(4x−x+2)=(−x2+7x−3)(3x+2)(5x−x2+2x−3)(4x−x+2)=(−x2+7x−3)(3x+2)

=−3x3−2x2+21x2+14x−9x−6=−3x3+19x2+5x−6=−3x3−2x2+21x2+14x−9x−6=−3x3+19x2+5x−6

h) (x+4)(x2−4x+16)=x3+43=x3+64(x+4)(x2−4x+16)=x3+43=x3+64h) (x−3y)(x2+3xy+9y2)=x3−(3y)3=x3−27y3(x−3y)(x2+3xy+9y2)=x3−(3y)3=x3−27y3.

1) (x−1)(x+3)=x2+3x−x−3=x2+2x−3(x−1)(x+3)=x2+3x−x−3=x2+2x−3.

Bài 3:

a) 2004−16=2004−4−12=2000−12=19882004−16=2004−4−12=2000−12=1988

b) 10,2.9,8−9,8.0,2+10,22−10,2.0,2