Question

Simplify the expression: (x^2 - 10x - 6) - [(-8x^2 + 11x - 1) + 5x^2 - 9x - 3]

a) -12x^2 - 1
b) -6x^2 - 19x - 9
c) -2x^2 + 21x + 3
d) -12x^2 - 19x - 9

Answer 1

To simplify the given algebraic expression, distribute the negative sign inside the brackets, remove the brackets, combine like terms, and you will get the simplified expression 4x^2 - 12x - 2.

Step-by-step explanation:

To simplify the expression: (x^2 - 10x - 6) - [(-8x^2 + 11x - 1) + 5x^2 - 9x - 3], we first distribute the negative sign inside the brackets:

• (x^2 - 10x - 6) - (-8x^2 + 11x - 1) - (5x^2 - 9x - 3)

We then remove the brackets and change the sign of each term inside:

• x^2 - 10x - 6 + 8x^2 - 11x + 1 - 5x^2 + 9x + 3

Next, we combine like terms:

• (x^2 + 8x^2 - 5x^2) + (-10x - 11x + 9x) + (-6 + 1 + 3)
• (4x^2) + (-12x) + (-2)

Thus, the expression simplifies to:

• 4x^2 - 12x - 2