Fill in the parentheses to create equivalent equations
1. -2x^2 ( ) = 4x^3 + 6x^2 - 2x^2
2. 3x^3 ( ) = 27x^5 - 9x^4
3. -5 ( ) = 10x^4 - 8x^2 - 5
for example
1. -2x^2 ( something) = 4x^3 + 6x^2 - 2x^2 = 4 x^3+ 4 x^2
so
something = (4x^3 + 4 x^2) / (-2 x^2)
= -2 x - 2
-2x^2 (-2x-3+1)
just divide by the indicated factor.
To create equivalent equations, we need to find the missing expressions in the parentheses that will balance both sides of the equation.
1. To balance both sides of the equation "-2x^2 ( ) = 4x^3 + 6x^2 - 2x^2" we need to fill in the parentheses with "+ 8x^2" since adding 8x^2 to the left side will give us "-2x^2 + 8x^2 = 6x^2". Therefore, the equation becomes:
-2x^2 + 8x^2 = 4x^3 + 6x^2 - 2x^2
2. To balance both sides of the equation "3x^3 ( ) = 27x^5 - 9x^4" we need to fill in the parentheses with "- 9x^3" since subtracting 9x^3 from the left side will give us "3x^3 - 9x^3 = -6x^3". Therefore, the equation becomes:
3x^3 - 9x^3 = 27x^5 - 9x^4
3. To balance both sides of the equation "-5 ( ) = 10x^4 - 8x^2 - 5" we need to fill in the parentheses with "+5" since adding 5 to the left side will give us "-5 + 5 = 0". Therefore, the equation becomes:
-5 + 5 = 10x^4 - 8x^2 - 5