\(a,x^2-20x+75\)
\(=x^2-20x+64+11\)
\(=x^2-2.x.10+8^2+11\)
\(=\left(x-8\right)^2+\sqrt{11}^2\)
\(=\left(x-8+\sqrt{11}\right)\left(x-8-\sqrt{11}\right)\)
\(b,x^2-y^2+5x+5y\)
\(=\left(x^2-y^2\right)+\left(5x+5y\right)\)
\(=\left(x-y\right)\left(x+y\right)+5\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+5\right)\)
a,x2−20x+75a,x2−20x+75
=x2−20x+64+11=x2−20x+64+11
=x2−2.x.10+82+11=x2−2.x.10+82+11
=(x−8)2+√112=(x−8)2+112
=(x−8+√11)(x−8−√11)=(x−8+11)(x−8−11)
b,x2−y2+5x+5yb,x2−y2+5x+5y
=(x2−y2)+(5x+5y)=(x2−y2)+(5x+5y)
=(x−y)(x+y)+5(x+y)=(x−y)(x+y)+5(x+y)
=(x+y)(x−y+5)
