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g ) \(4x^2\left(x-2y\right)-\left(4x+1\right)\left(2y-x\right)\)
\(=4x^2\left(x-2y\right)+\left(4x+1\right)\left(x-2y\right)\)
\(=\left(4x^2+4x+1\right)\left(x-2y\right)\)
\(=\left(2x+1\right)^2\left(x-2y\right)\)
h ) \(x^2-ax^2-y+ay+cx^2-cy\)
\(=x^2\left(1-a+c\right)-y\left(1-a+c\right)\)
\(=\left(x^2-y\right)\left(1-a+c\right)\)
A.(x+2y).(x+2y-1) = x^2 +4xy + 4y^2 - x - 2y
B. (x-2y).(x+2y-1) = x^2 - x - 4y^2 + 2y
C. (x-2y).(x-2y+1) = x^2 - 4xy + 4y^2 + x - 2y
D.(x+2y).(x-2y) = x^2 - 4y^2
=>....
\(a,3x-6y=3\left(x-2y\right)\)
\(b,\frac{2}{5}x^2+5x^3+x^2y=x^2\left(\frac{2}{5}+5x+y\right)\)
1, x2+3xy+2y2= x2+xy+2xy+2y2=x(x+y)+2y(x+y)=(x+2y)(x+y)
2, x(x+2)(x+3)(x+5)+9=x(x+5)(x+2)(x+3)+9=(x2+5x)(x2+5x+6)+9
Đặt x2+5x=t, ta có
t(t+6)+9=t2+6t+9=(t+3)2=(x2+5x+3)2=(x2+8)2
3, x2+2xy+y2+2x+2y-15=(x+y)2+2(x+y)-15=(x+y)2+2(x+y)+1-16=(x+y+1)2-42
= (x+y+1-4)(x+y+1+4)=(x+y-3)(x+y+5)
4, 4x4y4+1=4x4y4+4x2y2+1-4x2y2=(2x2y2+1)2-(2xy)2=(2x2y2+1-2xy)(2x2y2+1+2xy)
\(x\left(x+2\right)\left(x+3\right)\left(x+5\right)+9\)
\(=\left(x^2+5x+6\right)\left(x^2+5x\right)+9\)
Đặt \(t=x^2+5x\)ta được;
\(t\left(t+6\right)+9=t^2+6t+9\)
\(=\left(t+3\right)^2=\left(x^2+5x+3\right)^2\)
b)\(x^2+2xy+y^2+2x+2y-15\)
\(=\left(x+y+1\right)^2-4^2\)
\(=\left(x+y+1+4\right)\left(x+y+1-4\right)\)
\(=\left(x+y-3\right)\left(x+y+5\right)\)
c)\(4x^4y^4+1=\left(2x^2y^2-2xy+1\right)\left(2x^2y^2+2xy+1\right)\)
4x(x-2y)+8y(2y-x)
=4x(x-2y)-8y(x-2y)
=(4x-8y)(x-2y)
=4(x-2y)(x-2y)
=4(x-2y)^2
\(4x\left(x-2y\right)+8y\left(2y-x\right)\)
\(=\left(x-2y\right)\left(4x-8y\right)\)
\(=\left(x-2y\right)\left(x-2y\right).4\)\(=\left(x-2y\right)^2\)
\(\left(x+1\right)^4+\left(x^2+x+1\right)^2\)
\(=\left(x+1\right)^4+x^2\left(x+1\right)^2+2x\left(x+1\right)+1\)
\(=\left(x+1\right)^2.\left(2x^2+2x+1\right)+\left(2x^2+2x+1\right)\)
\(=\left(2x^2+2x+1\right)\left(x^2+2x+2\right)\)