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What must be subtracted from $3a^2-6ab-3b^2-1$ to get $4a^2-7ab-4b^2-1$?
To do: To find the number that should be substracted from $3a^2-6ab-3b^2-1$ to get $4a^2-7ab-4b^2-1$?
Solution:
Let the number to be subtracted is $x$
$3 a^{2} - 6 a b - 3 b^{2} - 1 - x = 4 a^{2} - 7 a b - 4 b^{2} + 1$
Bring x to the opposite side,
$3 a ^2 - 6 a b - 3 b ^2 - 1 - (4 a ^2 - 7 a b - 4 b ^2 + 1) = x$
Multiply - inside the brackets,
$3 a^2 - 6 a b - 3 b^2 - 1 - 4 a 2 + 7 a b + 4 b^2 - 1 = x$
$3 a^2 - 4 a^2 - 6 a b + 7 a b - 3 b^2 + 4 b^2 - 1 - 1 = x$
-$ a^2 + a b + b^ 2 - 2 = x$
Rewrite,
$x = - a^ 2 + a b + b^ 2 - 2$
So, $- a^ 2 + a b + b^ 2 - 2$ is to be subtracted from $3 a^2 - 6 a b - 3 b^2 - 1$ , to get
$4 a^2 - 7 a b - 4 b^2 + 1$