Bài 1:
\(a,413\left(413-26\right)+169\)
\(=413^2-26.413+13^2\)
\(=413^2-2.413.13+13^2\)
\(=\left(413-13\right)^2\)
\(=400^2\)
\(=160000\)
\(b,x^2+2x+1\)
\(=x^2+2.x.1+1^2\)
\(=\left(x+1\right)^2\)
\(=\left(99+1\right)^2\)
\(=100^2=10000\)
a) 9x2 - 36
= ( 3x)2 - 62
= ( 3x - 6)( 3x + 6)
b) ax - ay - bx + by
= a( x - y) - b( x - y)
= ( x - y)( a - b)
c) y3 - 4y2 + 3y
= y3 - y2 - 3y2 + 3y
= y2( y - 1) - 3y( y - 1)
= ( y - 1)( y2 - 3y)
= y( y - 3)( y - 1)
Bài2 :
a ) \(9x^2-36=\left(3x\right)^2-6^2=\left(3x-6\right)\left(3x+6\right)\)
b )\(ax-ay-bx+by=a\left(x-y\right)-b\left(x-y\right)=\left(x-y\right)\left(a-b\right)\)
c ) \(y^3-4y^2+3y=y^3-y^2-3y^2+3y=y^2\left(y-1\right)-3y\left(y-1\right)=\left(y-1\right)\left(y^2-3y\right)\)
Bài 2:
\(a,9x^2-36\)
\(=\left(3x\right)^2-6^2\)
\(=\left(3x-6\right)\left(3x+6\right)\)
\(b,ax-ay-bx+by\)
\(=\left(ax-ay\right)-\left(bx-by\right)\)
\(=a\left(x-y\right)-b\left(x-y\right)\)
\(=\left(x-y\right)\left(a-b\right)\)
\(c,y^3-4y^2+3y\)
\(=y\left(y^2-4y+3\right)\)
\(=y\left(y^2-3y-y+3\right)\)
\(=y\left[\left(y^2-3y\right)-\left(y-3\right)\right]\)
\(=y\left[y\left(y-3\right)-\left(y-3\right)\right]\)
\(=y\left(y-3\right)\left(y-1\right)\)
