Question

1. find the difference. $(4d - 6d^3 + 3d^2) - (10d^3 + 7d - 2)$

Explanation:

Step1: Distribute the negative sign

To subtract the second polynomial from the first, we distribute the negative sign to each term in the second polynomial:
$(4d - 6d^3 + 3d^2) - 10d^3 - 7d + 2$

Step2: Combine like terms

• For $d^3$ terms: $-6d^3 - 10d^3 = -16d^3$
• For $d$ terms: $4d - 7d = -3d$
• The $d^2$ term remains: $3d^2$
• The constant term remains: $+2$

Combining these, we get: $-16d^3 + 3d^2 - 3d + 2$

Answer:

$-16d^3 + 3d^2 - 3d + 2$