(27x 5 + 9x 4 - 18x 3) 9x 2

6. Simplify: i) (a + b)(5a – 3b) + (a – 3b)(a – b) ii) (a – b) (a² + b² + ab) – (a + b) (a² + b²– ab) iii) (b² – 49) (b + 7) + 3

Shkiper50 [21]

Step-by-step explanation:

(a + b)(5a – 3b) + (a – 3b)(a – b)

Expand each of the terms separately

That's

(a + b)(5a – 3b) = 5a² - 3ab + 5ab - 3b²

= 5a² + 2ab - 3b²

(a – 3b)(a – b) = a² - ab - 3ab + 3b²

= a² - 4ab + 3b²

<u>Add the terms</u>

That's

5a² + 2ab - 3b² + a² - 4ab + 3b²

<u>Group like terms</u>

5a² + a² + 2ab - 4ab - 3b² + 3b²

We have the answer as

(a – b) (a² + b² + ab) – (a + b) (a² + b²– ab)

Expand the terms separately

<u>For (a – b) (a² + b² + ab)</u>

Using the rule

x³ - y³ = (x - y)( x² + xy + y²) expand the expression

So we have

(a – b) (a² + b² + ab) = a³ - b³

<u>For (a + b) (a² + b²– ab)</u>

Using the rule

x³ + y³ = (x + y)( x² - xy + y²) expand the expression

We have

(a + b) (a² + b²– ab) = a³ + b³

Subtract the terms

That's

a³ - b³ - (a³ + b³)

Remove the parenthesis

a³ - b³ - a³ - b³

Group like terms

a³ - a³ - b³ - b³

We have the final answer as

(b² – 49) (b + 7) + 343

Expand the terms

That's

b³ + 7b² - 49b - 343 + 343

We have the final answer as

Hope this helps you

6 0

3 years ago

3(x+2)+5x how do i simplify that expression?

Andrew [12]

1st: do distributive property, that will give you 3x + 6 + 5x

2nd: combine like terms to simplify, this will give you 6 + 8x

6 0

2 years ago

Read 2 more answers

Simplify<br>6^7/6^5<br>leaving your answer in index form.

Juli2301 [7.4K]

Answer:

Step-by-step explanation: the and is 36.

8 0

2 years ago

A regular hexagon ABCDEF is shown……work out the size of angle x

denpristay [2]

Answer:

x=30

Step-by-step explanation:

Since this a regular hexagon, each angle measure is congruent.

A hexagon interior angles add to be

( ${6 - 2}) \times 180 = 720$

However, in the triangle, only part of angle b and angle f is in the triangle. However angle a is fully in the triangle so

Angle A=120.

So using the triangle interior theorem, angle b and f must add up to 180.

$120 + x + y = 180$

However, since this is a regular hexagon, the sides are equal so this is a isoceles triangle.

Using the base isoceles triangle theorem, angle b and angle f of the triangle must be equal so

$x = y$

$120 + 2x = 180$

$2x = 60$

$x = 30$

7 0

3 years ago

Read 2 more answers

Philip and Kevin are hoping to earn enough money to buy concert tickets for a show that costs $225 her concert tickets. Philip a

Zigmanuir [339]

Answer:

Kevin is going to be able to have enough money for the concert the fastest

Philip needs at least 4 weeks

Kevin needs at least 3 weeks

Step-by-step explanation:

<u>Philip</u>

$8.75/hour * 6 hours/weekend * 1 weekend/week = $52.5/week

$45 saved

Let's call x to the number of weeks Philip needs to reach $225.

52.5*x + 45 = 225

52.5*x = 225 - 45

x = 180/52.5

x = 3.43

He needs at least 4 weeks

<u>Kevin</u>

3 hours/day * $7.5/hour *3 days/week = $67.5/week

$30 saved

Let's call y to the number of weeks Kevin needs to reach $225.

67.5*y + 30 = 225

67.5*y = 225 - 30

y = 195/67.5

y = 2.9

He needs at least 3 weeks

6 0

3 years ago