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3 years ago

Write as a product 27a^3−(a−b)^3

Mathematics

1 answer:

jarptica [38.1K]3 years ago

6 0

Answer:

(2a +b)·(13a^2 -5ab +b^2)

Step-by-step explanation:

The factorization of the difference of cubes is a standard form:

(p -q)^3 = (p -q)(p^2 +pq +q^2)

Here, you have ...

p = 3a
q = (a-b)

so the factorization is ...

(3a -(a -b))·((3a)^2 +(3a)(a -b) +(a -b)^2) . . . . substitute for p and q

= (2a +b)·(9a^2 +3a^2 -3ab +a^2 -2ab +b^2) . . . . simplify a bit

= (2a +b)·(13a^2 -5ab +b^2) . . . . . . collect terms

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Question number 3 pls

marissa [1.9K]

Factoring f(x) would give a factor (x-1-2i), so you can divide f(x) by this, leaving (x-3)(x+4)(x-1+2i), so the other roots are:

x=3
x=-4
x=1-2i

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3 years ago

If a triangle is 12 inches high and has a 20 inch long hypotenuse then how wide is it?

Ber [7]

Answer:

The triangle should be 16 inches wide.

Step-by-step explanation:

$\text {Use the Pythagorean Theorem to solve for the leg.}\\a^2 + b^2 =c^2$

What we know:

One of the legs measures 12 inches.

The hypotenuse is 20 inches.

We need to solve for b. Solving for a while b is 12 would also be acceptable.

$12^2 + b^2 = 20^2 \text { OR } a^2 +12^2=20^2$

We will use the first equation.

$12^2 + b^2 = 20^2\\12 * 12 = 144\\20 * 20 = 400\\\\\boxed {144 + b^2 = 400}$

$\text {Subtraction property of equality: }\\144-144+ b^2 = 400-144\\\boxed {b^2 = 256}\\\\\text {Take the square root of 256: }\\\sqrt{256}=\sqrt{b^2} \boxed {16 = b}$

The triangle should be 16 inches wide.

3 0

3 years ago

Six less than two times a number is no more than 7

ziro4ka [17]

Answer:

n <=6.5

Step-by-step explanation:

Six less than two times a number is no more than 7

2n-6 <=7

Add 6 to each side

2n-6+6 <=7+6

2n <=13

Divide by 2

2n/2 <=13/2

n <=6.5

3 0

3 years ago

Last question needed for mastery please help thank you!

liraira [26]

A= P(1+r)^t, where P= initial value, r= interest rate in %, and t = number of years.
However, if there isa decrease in value, the formula becomes:

A= P(1-r)^t and in our case :

A = 30,000(1- 0.24)^t OR A = 30,000(0.76)^t

5 0

3 years ago

What number solves the equation x9=4?

MissTica

ANSWER: x=4/9
correct me if im wrong

5 0

3 years ago

Read 2 more answers