Simplify each of the following: 1.1 3m − n + 6n − 5m 1.2 ab(a2 −2b) 1.3 4d − d(2d + 2) 1.4 3(b − 2) + 6(b…

Question

Simplify each of the following: 1.1 3m − n + 6n − 5m 1.2 ab(a2 −2b) 1.3 4d − d(2d + 2) 1.4 3(b − 2) + 6(b + 1)

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QUESTION 1 1.1 Step 1: Group like terms together. (3m − 5m) + (−n + 6n) Step 2: Combine the like terms. −2m + 5n The simplified expression is * −2m + 5n × 1.2 Step 1: Distribute ab to each term inside the parenthesis. ab(a²) − ab(2b) Step 2: Multiply the terms. a¹⁺²b − 2ab¹⁺¹ a³b − 2ab² The simplified expression is * a³b − 2ab² * 1.3 Step 1: Distribute −d to each term inside the parenthesis. 4d − (d · 2d + d · 2) 4d − (2d² + 2d) Step 2: Remove the parenthesis by changing the sign of each term inside. 4d − 2d² − 2d Step 3: Combine like terms. (4d − 2d) − 2d² 2d − 2d² The simplified expression is * 2d − 2d² × 1.4 Step 1: Distribute 3 into the first parenthesis and 6 into the second parenthesis. (3 · b − 3 · 2) + (6 · b + 6 · 1) 3b − 6 + 6b + 6 Step 2: Group like terms together. (3b + 6b) + (−6 + 6) Step 3: Combine the like terms. 9b + 0 9b The simplified expression is * 9b *

Simplify each of the following: 1.1 3m - n + 6n - 5m 1.2 ab(a2 -2b) 1.3 4d - d(2d + 2) 1.4 3(b - 2) + 6(b + 1)

Answers

Step-by-step solution

Part 1

Part 1.1· 2 steps
$\text{} -2m + 5n \text{}$

Group like terms together.

Combine the like terms.

Part 1.2· 2 steps
$\text{} a^3b - 2ab^2 \text{}$

Distribute $ab$ to each term inside the parenthesis.

Multiply the terms.

Part 1.3· 3 steps
$\text{} 2d - 2d^2 \text{}$

Distribute $-d$ to each term inside the parenthesis.

Remove the parenthesis by changing the sign of each term inside.

Combine like terms.

Part 1.4· 3 steps
$\text{} 9b \text{}$

Distribute 3 into the first parenthesis and 6 into the second parenthesis.

Group like terms together.

Combine the like terms.

Try one yourself

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More Mathematics Questions

Simplify each of the following: 1.1 3m - n + 6n - 5m 1.2 ab(a2 -2b) 1.3 4d - d(2d + 2) 1.4 3(b - 2) + 6(b + 1)

Answers

Step-by-step solution

Part 1

Part 1.1· 2 steps−2m+5n\text{} -2m + 5n \text{}−2m+5n

Group like terms together.

Combine the like terms.

Part 1.2· 2 stepsa3b−2ab2\text{} a^3b - 2ab^2 \text{}a3b−2ab2

Distribute ababab to each term inside the parenthesis.

Multiply the terms.

Part 1.3· 3 steps2d−2d2\text{} 2d - 2d^2 \text{}2d−2d2

Distribute −d-d−d to each term inside the parenthesis.

Remove the parenthesis by changing the sign of each term inside.

Combine like terms.

Part 1.4· 3 steps9b\text{} 9b \text{}9b

Distribute 3 into the first parenthesis and 6 into the second parenthesis.

Group like terms together.

Combine the like terms.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Part 1.1· 2 steps
$\text{} -2m + 5n \text{}$

Part 1.2· 2 steps
$\text{} a^3b - 2ab^2 \text{}$

Distribute $ab$ to each term inside the parenthesis.

Part 1.3· 3 steps
$\text{} 2d - 2d^2 \text{}$

Distribute $-d$ to each term inside the parenthesis.

Part 1.4· 3 steps
$\text{} 9b \text{}$