Question

6. Find the product of (a - 2b + 3c) and (2a + b - 3c).

Answer 1

Answer:

The product of (a - 2b + 3c) and (2a + b - 3c) is$2a^2 -3ab +3ac +9 bc - 2b^2 -9c^2$ .

Step-by-step explanation:

$(a - 2b + 3c) x (2a + b - 3c)\\= a (2a + b - 3c) -2b(2a + b - 3c) + 3c (2a + b - 3c)\\= a(2a) + a(b) - a(3c) - 2b(2a) - 2b (b) - 2b (-3c) + 3c(2a) + 3c(b) + 3c (-3c)\\= 2a^2 + ab - 3ac -4ab - 2b^2 + 6 bc +6ac + 3bc -9c^2$

Arrange like terms

$= 2a^2 + ab -4ab - 3ac+6ac + 6 bc + 3bc - 2b^2 -9c^2\\= 2a^2 -3ab +3ac +9 bc - 2b^2 -9c^2$

Answer 2

The answer is " ( 2a^2 - 2b^2 - 9c^2 - 3ab + 3ac + 9bc ) "

Step-by-step explanation:

( a - 2b + 3c ) * ( 2a + b - 3c )

= ( 2a^2 + ab - 3ac - 4ab - 2b^2 + 6bc + 6ac + 3cb - 9c^2 )

= ( 2a^2 - 2b^2 - 9c^2 - 3ab + 3ac + 9 bc )

Therefore

( a - 2b + 3c ) * ( 2a + b - 3c ) = ( 2a^2 - 2b^2 - 9c^2 - 3ab + 3ac + 9bc )