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\(20x^2y-12x^3=4x^2\left(5y-3x\right)\)
\(8x^4+12x^2y^4-16x^3y^4=4x^2\left(2x^2+3y^4-4xy^4\right)\)
\(6x^3-9x^2=3x^2\left(2x-3\right)\)
\(4xy^2+8xy^2=12xy^2\)
\(3x\left(x+1\right)-5\left(x+1\right)=\left(3x-5\right)\left(x+1\right)\)
\(20x^2y-12x^3\)
\(=4x^2\left(5y-3x\right)\)
\(8x^4+12x^2y^4-16x^3y^4\)
\(=4x^2\left(2x^2+3y^4-4xy^4\right)\)
1.a)\(20x-5y=5\left(4x-y\right)\)
b)\(5x\left(x-1\right)-3x\left(x-1\right)=\left(5x-3x\right)\left(x-1\right)=2x\left(x-1\right)\)
c)\(x\left(x+y\right)-6x-6y=x\left(x+y\right)-6\left(x+y\right)=\left(x-6\right)\left(x+y\right)\)
d)\(6x^3-9x^2=3x^2\left(2x-3\right)\)
e)\(4x^2y-8xy^2+10x^2y^2=2xy\left(2x-8y+10xy\right)\)
g)\(20x^2y-12x^3=4x^2\left(5y-3x\right)\)
h)\(8x^4+12x^2y-16x^3y^4=4x^2\left(2x^2+12y-16xy^4\right)\)
2.a)\(3x\left(x+1\right)-5y\left(x+1\right)=\left(3x-5y\right)\left(x+1\right)\)
b)\(3x\left(x-6\right)-2\left(x-6\right)=\left(3x-2\right)\left(x-6\right)\)
c)\(4y\left(x-1\right)-\left(1-x\right)=4y\left(x-1\right)+\left(x-1\right)=\left(4y+1\right)\left(x-1\right)\)
d)\(\left(x-3\right)^3+3-x=\left(x-3\right)^3-\left(x-3\right)=\left(x-3\right)\left[\left(x-3\right)^2-1\right]=\left(x-3\right)\left(x-2\right)\left(x-4\right)\)
e)\(7x\left(x-y\right)-\left(y-x\right)=7x\left(x-y\right)+\left(x-y\right)=\left(7x+1\right)\left(x-y\right)\)
h)\(3x^3\left(2y-3z\right)-15x\left(2y-3z\right)^2=3x\left(2y-3z\right)\left[x^2-5\left(2y-3z\right)\right]\)
k)Sai đề: \(3x\left(z+2\right)+5\left(-z-2\right)=3x\left(z+2\right)-5\left(z+2\right)=\left(3x-5\right)\left(z+2\right)\)
l)\(18x^2\left(3+x\right)+3\left(x+3\right)=3\left(x+3\right)\left(6x^2+1\right)\)
m)\(14x^2y-21xy^2+28x^2y^2=7xy\left(2x-3y+4xy\right)\)
n)\(10x\left(x-y\right)-8y\left(y-x\right)=10x\left(x-y\right)+8y\left(x-y\right)=2\left(5x+4y\right)\left(x-y\right)\)
bài 1 điền vào chỗ trống
a) x2 + 4x + 4
= (x + 2)2
b) x2 - 8x + 16
= (x - 4)2
c) x3 +12x2 + 48x + 64
= (x + 4)3
d) x3 - 6x + 12x - 8
= (x - 2)3
e) x2 + 2x + 1
= (x + 1)2
f) x2 - 1
= (x - 1)(x + 1)
g) x2 - 4x + 4
= (x - 2)2
h) x2 - 4
= (x - 2)(x + 2)
i) x2 + 6x + 9
= (x + 3)2
j) 4x2 - 9
= (2x - 3)(2x + 3)
k) 16x2 - 8x + 1
= (4x - 1)2
l) 9x2 + 6x + 1
= (3x + 1)2
m) 36x2 + 36x + 9
= (6x + 3)2
n) x3 + 27
= (x + 3)(x2 - 3x + 9)
o) 17x3 + 27 (Đề sai)
a) \(4x^2-81=\left(2x\right)^2-9^2=\left(2x-9\right)\left(2x+9\right)\)
b) \(3\left(x-y\right)+5x\left(y-x\right)=3\left(x-y\right)-5x\left(x-y\right)=\left(x-y\right)\left(3-5x\right)\)
c) \(x\left(x+y\right)+6x+6y=x\left(x+y\right)+6\left(x+y\right)=\left(x+y\right)\left(x+6\right)\)
d) \(20x-5y=5\left(4x-y\right)\)
e) \(=2xy\left(5xy-4y+2y\right)\)
g) \(4xy+8xyz=4xy\left(1+2z\right)\)
a) \(5x^2-20x+20y-5y^2\)
\(=5\left(x^2-y^2\right)-20\left(x-y\right)\)
\(=5\left(x-y\right)\left(x+y\right)-20\left(x-y\right)\)
\(=5\left(x-y\right)\left(x+y-4\right)\)
b) \(\left(x-y+5\right)^2-2\left(x-y+5\right)+1\)
\(=\left(x-y+5-1\right)^2\)
\(=\left(x-y+4\right)^2\)
c) \(7x-7y+5x-5y\)
\(=7\left(x-y\right)+5\left(x-y\right)\)
\(=\left(x-y\right)\left(7+5\right)\)
\(=12\left(x-y\right)\)
d) \(16x^2-8x+1\)
\(=\left(4x\right)^2-2.4x+1\)
\(=\left(4x-1\right)^2\)
e) \(100x^2-\left(x^2+25\right)^2\)
\(=\left(10x\right)^2-\left(x^2+25\right)^2\)
\(=\left(10x-x^2+25\right)\left(10x+x^2+25\right)\)
\(=\left(10x-x^2+25\right)\left(x+5\right)^2\)
\(a,6x^3-9x^2=3x^2\left(2x-3\right)\)
\(b,4x^2y-8xy^2+10x^2y^2=2xy\left(2x-4y+5xy\right)\)
\(c,20x^2y-12x^3=4x^2\left(5y-3x\right)\)
\(d,4xy^2+8xyz=4xy\left(y+2z\right)\)
a) 7x+7y=7(x+y)
b) 2x2y-6xy2=2xy(x-3y)
c)3x(x-1)+7x2(x-1)=x(x-1)(3+7x)
d)3x(x-4)+5x2(4-x)=(x-4)(3x-5x2)
=x(x-4)(3-5x)
e)6x4-9x3=3x3(2x-3)
f)5y8-15y6=5y6(y2-3)
a, 20x - 5y = 5(4x - y)
b, 4x2 - 8xy2 + 10x2y = 2x(2x - 4y2 + 5xy)
c, 5x (x - 1) - 3x (x - 1) = (5x - 3x) (x - 1) = 2x (x - 1)
d, x (x + y) - 6x - 6y = x (x + y) - (6x + 6y) = x (x + y) - 6 (x + y) = (x - 6) (x + y)
e, x4 - y4 = (x2)2 - (y2)2 = (x2 - y2) (x2 + y2) = [(x + y) (x - y)] (x2 + y2)
f, x2 - 4y2 = x2 - (2y)2 = (x - 2y) (x + 2y)
g, 27x3 - 64 = (3x)3 - 43 = (3x - 4) (9x2 + 12x + 16)
h, (x +1)2 - 16 = (x +1)2 - 42 = (x + 1 + 4) (x + 1 - 4) = (x + 5) (x - 3)
i, (3x + 1)2 - (x - 2)2 = (3x + 1 - x + 2) (3x + 1 + x - 2) = (2x + 3) ( 4x - 1)
\(a,20x-5y\)
\(=5\left(4x-y\right)\)
\(b,5x\left(x-1\right)-3x\left(x-1\right)\)
\(=\left(x-1\right)\left(5x-3x\right)=\left(x-1\right).2x\)
\(c,x\left(x+y\right)-6x-6y\)
\(=x\left(x+y\right)-6\left(x+y\right)\)
\(=\left(x-6\right)\left(x+y\right)\)
\(d,6x^3-9x^2\)
\(=3x^2\left(2x-3\right)\)
\(e,4x^2y-8xy^2+10x^2y^2\)
\(=2xy\left(2x-4y+5xy\right)\)
\(g,20x^2y-12x^3\)
\(=4x^2\left(5y-3x\right)\)
\(h,8x^4+12x^2y^4-16x^3y^4\)
\(=4x^2\left(2x^2+3y^2-4xy^4\right)\)
\(k,4xy^3+8xyz\)
\(=4xy\left(y^2+2z\right)\)
a. 20x - 5y
= 5(4x - y)
b. 5x(x - 1) - 3x(x - 1)
= (x - 1).2x
c. x(x + y) - 6x - 6y
= (x - 6)(x + y)
d. 6x3 . 9x2
= 3x2 (2x - 3)
e. 4x2y - 8xy2 + 10x2y2
= 2xy(2x - 4y + 5xy)
g. 20x2y - 12x3
= 4x2 (5y - 3x)
h. 8x4 + 12x2y4 - 16x3y4
= 4x2 (2x2 +3y2 - 4xy4)
k. 4xy2 + 8xyz
= 4xy (y2 + 2z)