Question

algebra & geometry review

1. subtract.

((7d^2 + 8d - 7) - (d^2 + 4d + 4))

1. subtract.

((4z^2 - 1) - (5z^3 - 7z - 5))

1. add.

((9d^3 + 4d + 2) + (-4d^3 + 3d^2 - 9d))

Explanation:

Problem 1:

Step1: Distribute the negative sign

$(7d^2 + 8d - 7) - (d^2 + 4d + 4) = 7d^2 + 8d - 7 - d^2 - 4d - 4$

Step2: Combine like terms for \(d^2\)

$7d^2 - d^2 = 6d^2$

Step3: Combine like terms for \(d\)

$8d - 4d = 4d$

Step4: Combine constant terms

$-7 - 4 = -11$

Step5: Combine all terms

$6d^2 + 4d - 11$

Step1: Distribute the negative sign

$(4z^2 - 1) - (5z^3 - 7z - 5) = 4z^2 - 1 - 5z^3 + 7z + 5$

Step2: Rearrange terms by degree

$-5z^3 + 4z^2 + 7z + (-1 + 5)$

Step3: Combine constant terms

$-1 + 5 = 4$

Step4: Combine all terms

$-5z^3 + 4z^2 + 7z + 4$

Step1: Remove parentheses

$(9d^3 + 4d + 2) + (-4d^3 + 3d^2 - 9d) = 9d^3 + 4d + 2 - 4d^3 + 3d^2 - 9d$

Step2: Combine like terms for \(d^3\)

$9d^3 - 4d^3 = 5d^3$

Step3: Combine like terms for \(d\)

$4d - 9d = -5d$

Step4: Combine all terms

$5d^3 + 3d^2 - 5d + 2$

Answer:

$6d^2 + 4d - 11$

Problem 2: