Đáp án:

 a.3x³−5x²+7xa.3x³−5x²+7x

b.−4x²y−10x²y+2xyb.−4x²y−10x²y+2xy

c.−x³+2x²+29x+20c.−x³+2x²+29x+20

d.2x⁴−3x³+2x²+3x−4d.2x⁴−3x³+2x²+3x−4

e.x²−4y²e.x²−4y²

h.2x²−6x+13h.2x²−6x+13

g.3xy⁴−12y²+2x²yg.3xy⁴−12y²+2x²y 

f.−2x²y³+y−3f.−2x²y³+y−3

Giải thích các bước giải:

 a.3x.(x²−5x+7)a.3x.(x²−5x+7)

=3x³−5x²+7x=3x³−5x²+7x

b.−2xy.(2x³+5x−1)b.−2xy.(2x³+5x−1)

=−4x⁴y−10xy²+2xy=−4x⁴y−10xy²+2xy

c.(x+4).(−x²+6x+5)c.(x+4).(−x²+6x+5)

=−x³+6x²+5x−4x²+24x+20=−x³+6x²+5x−4x²+24x+20

=−x³+2x²+29x+20=−x³+2x²+29x+20

d.(x²−1).(2x²−3x+4)d.(x²−1).(2x²−3x+4)

=2x⁴−3x³+4x²−2x²+3x−4=2x⁴−3x³+4x²−2x²+3x−4

=2x⁴−3x³+2x2+3x−4=2x⁴−3x³+2x2+3x−4

$e.(x+2y).(x-2y)$

=x²−(2y)²=x²−(2y)²

=x²−4y²=x²−4y²

h.(3x−1)²−7(x²+2)h.(3x−1)²−7(x²+2)

=9x²−6x+1−7x²−14=9x²−6x+1−7x²−14

=2x²−6x+13=2x²−6x+13

g.(6x²g.(6x²y⁵−xy³+4x³y²):2xy−xy³+4x³y²):2xy

=3xy⁴−12y²+2x²y=3xy⁴−12y²+2x²y 

f.(−12x³y⁴+6xy²−18xy):6xyf.(−12x³y⁴+6xy²−18xy):6xy

=−2x³y³+y−3

a)

Đơn thức đồng dạng: 

 5x²y và  x²y

-x và 2/3x

–2xy² và 5xy²

b) 5xy² + 10xy²+3/4 xy²–12xy²

= ( 5+10 + 3/4 - 12 ) .xy²

= \(\dfrac{15}{4}xy^2\)

`a)`Các cặp đơn thức đồng dạng là:

 `+,5x^2y` ; `x^2y`

 `+,-x` ; `2/3x`

 `+,-2xy^2` ; `5xy^2`

________________________________________

`b)5xy^2+10xy^2+3/4xy^2-12xy^2`

`=(5+10+3/4-12)xy^2`

`=15/4xy^2`

a) 6x⁴ - 9x³ = 3x³(2x - 3)

b) 5y¹⁰ + 15y⁶ = 5y⁶(y⁴ + 3)

c) x² - 6xy + 9y² = x² - 6xy + (3y)² = (x - 3y)²

e) x³ - 64 = x³ - 4³ = (x - 4)(x² + 4x + 16)

f) 125x³ + y⁶ = (5x)³ + (y²)³ = (5x + y²)(25x² + 5y² + y⁴)

g) 0,125(a + 1)³ - 1 = [0,5(a + 1)]³ - 1³ = (0,5a + 0,5)³ - 1³ = (0,5a + 0,5 - 1)[(0,5a + 0,5)² + (0,5a + 0,5) + 1) = (0,5a - 0,5)(0,25a^2 + 0,5 a + 0,25 + 0,5a + 0,5 + 1) = (0,5a - 0,5)(0,25a² + 1,75 + a)

h) 3x² - 12y² = 3(x² - 4y²) = 3[x² - (2y)² ] = 3(x - 2y)(x + 2y)

`(x-5y)(3x^2+y^2+5xy)`

`=x(3x^2+y^2+5xy)-5y(3x^2+y^2+5xy)`

`=3x^3+xy^2+5x^2y-15x^2y-5y^3-25xy^2`

`=3x^3-5y^3-24xy^2-10x^2y`

\(\left(x-5y\right)\left(3x^2+y^2+5xy\right)\)

\(=3x^3+xy^2+5x^2y-15x^2y-5y^3-25xy^2\)

\(=3x^3-5y^3+xy^2-25xy^2+5x^2y-15x^2y\)

\(=3x^3-y^3-24xy^2-10x^2y\)

A = 3x² + 5y³ - 5xy² - 3xy + 2017

= (3x² - 3xy) + (5y³ - 5xy²) + 2017

= 3x(x - y) + 5y²(y - x) + 2017

= 3x(x - y) - 5y²(x - y) + 2017

= (x - y)(3x - 5y²) + 2017 

= 0 + 2017 = 2017 (Vì x - y) = 0

a,3x³y³-15x²y²=3x²y²(xy-5)

b,2x(x-5y)+8y(5y-x)=2x(x-5y)-8y(x-5y)=(x-5y).(2x-8y)

c,(3x-1)²-16=(3x-1)²-4²=(3x-1+4)(3x-1-4)=(3x+3)(3x-5)

d,x³-3x²+3x-1=x³-1-(3x²+3x)=x³-1-3x(x+1)=(x³-1-3x)(x+1)

e,125x³+1=(5x)³+1³=(5x+1)(25x²-5x.1+1²)

f,x³+6x²y+12xy²+8y³=x³+3.x².2y+3.x.(2y)²+(2y)³=(x+2y)³

Đề lỗi rồi. Bạn xem lại.

a) 2x-5y+4y+2x

=4x+y

Tai x=3 y=-12 thi

4x3+(-12)=12-12=0

b)3x+4y-2x-3y

b)3x+4y-2x-3y

=x+y

Tai x-2; y=-5 thi

2+(-5)=2-5=-3