Question

OBLICZ:

f) 6(y-2)(y+2)+(3y-2)^{2} - 4 (y-1)^{2}

g) 2(2a+b)^{2} - (2b +a)^{2} + (a-2b)^{2}

h) (4x - y)^{2} + (2y-3x)^{2} - (5x-y)^{2} (5x+y)

Answer 1

f) 6(y-2)(y+2)+(3y-2)^{2} - 4 (y-1)^{2}=6(y^{2}-4)+9y^{2}+4-12y-4(y^{2}+1-2y)=

=6y^{2}-24+9y^{2}+4-12y-4y^{2}-4+8y=11y^{2}-4y-24

g) 2(2a+b)^{2} - (2b +a)^{2} + (a-2b)^{2}=

=2(4a^{2}+b^{2}+4ab)-(4b^{2}+a^{2}+4ab)+a^{2}+4b^{2}-4ab=

=8a^{2}+2b^{2}+8ab-4b^{2}-a^{2}-4ab+a^{2}+4b^{2}-4ab=8a^{2}+2b^{2}

h) (4x - y)^{2} + (2y-3x)^{2} - (5x-y)^{2} (5x+y)=

=16x^{2}+y^{2}-8xy+4y^{2}+9x^{2}-12xy-(25x^{2}+y^{2}-10xy)(5x+y)=

=25x^{2}+5y^{2}-20xy-(125x^{3}+25x^{2}y+5xy^{2}+y^{3}-50x^{2}y-10xy^{2})=

=25x^{2}+5y^{2}-20xy-125x^{3}-25x^{2}y-5xy^{2}-y^{3}+50x^{2}y+10xy^{2}=

=25x^{2}+5y^{2}-20xy-125x^{3}+25x^{2}y+5xy^{2}-y^{3}

Mam nadzieję, że się nie pomyliłem w liczeniu :)