Question

Expand the following (-2a-b+3c)^2​

Answer 1

$\huge\bold\purple{QUESTION}$

Expand the following (-2a-b+3c)²

$\huge\bold\red{ANSWER}$

LET x=(-2a)

y=(-b)

z=(3c)

WE NEED TO FIND OUT (x+y+z)²

=x²+y²+z²+2(xy+yz+zx)

=(-2a)²+(-b)²+(3c)²+2[{(-2a)×(-b)}+{(-b)×(3c)}+{(3c)×(-2a)}]

=4a²+b²+9c²+2(2ab-3bc-6ac)

=4a²+b²+9c²+4ab-6bc-12ac

$\bold\blue{ADDITIONAL\: \: INFORMATION}$

• a²+b²+2ab=(a+b)²

• a²+b²-2ab=(a-b)²

• a²-b²=(a+b)(a-b)

• a³+b³=(a+b)(a²+b²-ab)

• a³-b³=(a-b)(a²+b²+ab)

• a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)

• a³+b³+3ab(a+b)=(a+b)³

• a³-b³-3ab(a-b)=(a-b)³