Question

Answer 1

a.

\(45^2+33^2-22^2+90.33=45^2+33^2+2.45.33-22^2\)

\(=(45+33)^2-22^2=78^2-22^2=(78-22)(78+22)=56.100=5600\)

b.

\(111^2-137^2-48^2+96.137\)

\(=111^2-(137^2+48^2-2.137.48)=111^2-(137-48)^2\)

\(=111^2-89^2=(111-89)(111+89)=22.200=4400\)

Answer 2

c.

$x^2-3x-3y+xy=x(x+y)-3(x+y)=(x-3)(x+y)=(\frac{1}{3}-3)(\frac{1}{3}+\frac{8}{3})$

$=-8$

d.

$(2x-1)^2+2(2x-1)(3x+1)+(3x+1)^2=[(2x-1)+(3x+1)]^2$

$=(5x)^2=(5.\frac{-1}{5})^2=(-1)^2=1$
e.

$x^2-2xy+y^2-10x+10y=(x-y)^2-10(x-y)$

$=(x-y)(x-y-10)=9(9-10)=9(-1)=-9$