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\(a.10x\left(x-y\right)-6y\left(y-x\right)\\ =10x\left(x-y\right)+6y\left(x-y\right)\\ =\left(10x-6y\right)\left(x-y\right)\\ =2\left(5x-3y\right)\left(x-y\right)\)
\(b.14x^2y-21xy^2+28x^3y^2\\ =7xy\left(x-y+xy\right)\)
\(c.x^2-4+\left(x-2\right)^2\\ =\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2\\ =\left(x-2\right)\left(x+2+x-2\right)\\ =2x\left(x-2\right)\)
\(d.\left(x+1\right)^2-25\\ =\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)
\(x^2+4x+4=\left(x+2\right)^2 \)
\(4x^2-4x+1=\left(2x-1\right)^2\)
\(c\left(x+1\right)-y\left(x+1\right)=\left(x+1\right)\left(c-y\right)\)
\(x^3-3x^2+3x-1+27y^3=\left(x-1\right)^3+27y^3=\left(x-1+3y\right)\left(x^2-2x+1-3xy+3y+9y^2\right)\)
a) \(2x^2-2y^2=2\left(x^2-y^2\right)=2\left(x-y\right)\left(x+y\right)\)
b) \(x^2+2x+1-y^2=\left(x+1\right)^2-y^2=\left(x+y+1\right)\left(x-y+1\right)\)
c) \(x^2-4x=x\left(x-4\right)\)
d) \(x^2+10x+25=x^2+2.5x+5^2=\left(x+5\right)^2\)
e) \(x^2-2xy+y^2-9=\left(x-y\right)^2-3^2=\left(x-y+3\right)\left(x-y-3\right)\)
\(2x^2-2y^2=2.\left(x^2-y^2\right)=2.\left(x-y\right)\left(x+y\right)\)
\(x^2+2x+1-y^2=\left(x+1\right)^2-y^2=\left(x+1-y\right)\left(x+1+y\right)\)
\(x^2-4x=x.\left(x-4\right)\)
\(x^2+10x+25=x^2+2.x.5+5^2=\left(x+5\right)^2\)
\(x^2-2xy+y^2-9=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\)
Tham khảo nhé~
d: \(=\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)
a) \(x^2-81=\left(x-9\right)\left(x+9\right)\)
b) \(4x^2-25=\left(2x-5\right)\left(2x+5\right)\)
c) \(x^4-y^4=\left(x^2-y^2\right)\left(x^2+y^2\right)=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\)
d) \(x^2+6xy+9y^2=\left(x+3y\right)^2\)
e) \(6x-9-x^2=-\left(x^2-6x+9\right)=-\left(x-3\right)^2\)
f) \(x^2-4x^2+4y^2+4xy=\left(x^2+4xy+4y^2\right)-4x^2=\left(x+2y\right)^2-4x^2\\ =\left(x+2y+2x\right)\left(x+2y-2x\right)=\left(3x+2y\right)\left(2y-x\right)\)
g) \(\left(a+b\right)^3+\left(a-b\right)^3=\left(a+b+a-b\right)\left[\left(a+b\right)^2-\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)
\(=2a\left(a^2+2ab+b^2-a^2+b^2+a^2-2ab+b^2\right)=2a\left(a^2+3b^2\right)\)
h) \(\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1+x+1\right)\left(3x+1-x-1\right)\\ =\left(4x+2\right)\cdot2x=4x\left(2x+1\right)\)
a) Kết quả 2x(2x – 3). b) Kết quả xy( x 2 – 2xy + 5).
c) Kết quả 2x(x + 1)(x + 4). d) Kết quả 2 5 ( y − 1 ) ( x + y ) .
a, \(25\left(x-2\right)^2-100\left(y-3\right)^2\)
\(=\left(5x-10\right)^2-\left(10y-30\right)^2\)
\(=\left(5x-10-10y+30\right)\left(5x-10+10y-30\right)\)
\(=\left(5x-10y+20\right)\left(5x+10y-40\right)\)
\(=25\left(x-2y+4\right)\left(x+2y-8\right)\)
b, \(4\left(x+3\right)^2-9\left(x+2\right)^2\)
\(=\left(2x+6\right)^2-\left(3x+6\right)^2\)
\(=\left(2x+6-3x-6\right)\left(2x+6+3x+6\right)\)
\(=-x\left(5x+12\right)\)
c, \(x^2-10x-y^2+25\)
\(=\left(x-5\right)^2-y^2\)
\(=\left(x-y-5\right)\left(x+y-5\right)\)
d, \(x^2-4x-y^2+4\)
\(=\left(x-2\right)^2-y^2\)
\(=\left(x-y-2\right)\left(x+y-2\right)\)
e, \(\left(x^2+2\right)^2-2\left(x^2+2\right)+1\)
\(=\left(x^2+2-1\right)^2\)
\(=\left(x^2+1\right)^2\)