Question

4.Разложите на множители выражение: 1) x-3y+x² -9y² 2) 1-x²+10xy-25y² 3)(x+5)³ -64

Answer 1

1) х-3у+х²-9у²=(х-3у)+(х²-9у²)=
=(х-3у)+(х²-(3у)²)=(х-3у)+(х-3у)(х+3у)=
=(х-3у)(1+х+3у)

2) 1-х²+10ху-25у²=1-(х²-10ху-25у²)=
=1-(х-у)²=(1+х-у)(1-х+у)

3) (х+5)³-64=(х+5)³-4³=
=(х+5-4)((х+5)²+(х+5)•4+4²)=
=(х+1)(х²+10х+25+4х+20+16)=
=(х+1)(х²+14х+61)