Question 1

$\bold{(10x - 6x³ + 8x²) - (5x² + 12x³ - 4)}$

Question 2

Answer:

-18x^3+3x^2+10x+4

Step-by-step explanation:

Given:

(10x-6x^3+8x^2)-(5x^2+12x^3-4)

Apply the rule (a) = a:

$\implies 10x-6x^3+8x^2-(5x^2+12x^3-4)$

$\textsf{Use the distributive law} \quad -(a+b)=-a-b:$

$\implies 10x-6x^3+8x^2-5x^2-12x^3-(-4)$

Apply the rule -(-a) = a:

$\implies 10x-6x^3+8x^2-5x^2-12x^3+4$

Collect like terms:

$\implies -6x^3-12x^3+8x^2-5x^2+10x+4$

Combine like terms:

$\implies -18x^3+3x^2+10x+4$

Question 3

Answer:

$\boxed{\sf -18x^3+3x^2+10x+4}$

Step-by-step explanation:

$\rightarrow \sf (10x - 6x^3 + 8x^2) - (5x^2 + 12x^3 - 4)$

distribute

$\rightarrow \sf 10x - 6x^3 + 8x^2 - 5x^2 - 12x^3 + 4$

collect terms

$\rightarrow \sf -6x^3-12x^3+3x^2+10x+4$

add similar terms

$\rightarrow \sf -18x^3+3x^2+10x+4$

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