Which is equivalent to (4xy – 3z)2, and what type of special product is it?16x2y2 + 9z2, the difference of squares
16x2y2 + 9z2, a perfect square trinomial
16x2y2 – 24xyz + 9z2, the difference of squares
16x2y2 – 24xyz + 9z2, a perfect square trinomial

Answers

Answer 1

Answer: (4xy - 3z)²

(4xy - 3z)(4xy - 3z)
4xy(4xy - 3z) - 3z(4xy - 3z)
16x²y² - 12xyz -12xyz + 9z²

16x²y² - 24xyz + 9z², a perfect square trinomial.

Answer 2

Answer:

The correct option is $\boxed{{\mathbf{Option D}}}$ .

Further explanation:

The binomial algebraic expression is an algebraic expression that consists two terms and it is separated by plus or minus.

Binomial expression can be mathematically expressed as,

$a + b$

The trinomial algebraic expression is an algebraic expression that consists three terms and it is separated by plus or minus.

Trinomial expression can be mathematically expressed as,

$a + b + c$

Here, $a,b{\text{ and }}c$ are the real numbers.

The square of the binomial $a + b$ can be written as,

${\left( {a + b} \right)^2} = \left( {a + b} \right)\left( {a + b} \right)$

Given:

The given algebraic expression is ${\left( {4xy - 3z} \right)^2}$ .

Step by step explanation:

Step 1:

The square of the binomial $a + b$ can be written as,

${\left( {a + b} \right)^2} = \left( {a + b} \right)\left( {a + b} \right)$

Similarly, the expression ${\left( {4xy - 3z} \right)^2}$ can be written as,

$\begin{aligned}{\left( {4xy - 3z} \right)^2} &= \left( {4xy - 3z} \right)\left( {4xy - 3z} \right) \n&= 4xy\left( {4xy - 3z} \right) - 3z\left( {4xy - 3z} \right) \n\end{aligned}$

Step 2:

The distributive property can be used to solve the square of the binomial.

The distributive property can be expressed as,

$a\left( {b + c} \right) = ab + ac$

Now apply the distributive property to solve the expression ${\left( {4xy - 3z} \right)^2}$ .

$\begin{aligned}{\left( {4xy - 3z} \right)^2} &= 4xy\left( {4xy - 3z} \right) - 3z\left( {4xy - 3z} \right) \n&= 16{x^2}{y^2} - 12xyz - 12xyz + 9{z^2} \n&= 16{x^2}{y^2} - 24xyz + 9{z^2} \n\end{aligned}$

Therefore, the expression $16{x^2}{y^2} - 24xyz + 9{z^2}$ is the perfect square of the binomial $\left( {4xy - 3z} \right)$ .

The expression $16{x^2}{y^2} - 24xyz + 9{z^2}$ is the trinomial.

Thus, option D a perfect square trinomial $16{x^2}{y^2} - 24xyz + 9{z^2}$ is correct.

Learn more:

Learn more about the function is graphed below brainly.com/question/9590016
Learn more about the symmetry for a function brainly.com/question/1286775
Learn more about midpoint of the segment brainly.com/question/3269852

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Algebraic expression

Keywords: binomial, polynomial, algebraic expression, difference, product, trinomial, distributive property, equivalent, expression, terms, plus, separated, multiply, minus, addition

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Which function represents a horizontal shift of ƒ(x) = 5(2)^3x by 4 units to the right?a. y = 0
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d. y = 5

Answers

General Idea:

Say if f(x) is the parent function, then f(x-c) represents transformation described as horizontal translation or shift of f(x) by ' c ' units to the right.

Applying the concept:

Here we are given a function $f(x)=5(2)^(3x)$ , after the transformation of horizontal shift of 4 units to the right, the function will be given as below:

$f(x)=5(2)^(3(x-4))=5(2^(3))^(x-4)=5(8)^(x-4) \n or\n f(x)=5(2)^(3x-12)$

Solve for x.
3(x + 5) - 2(x + 2) = 20

Answers

3(x + 5) - 2(x + 2) = 20

Distribute the 3 and -2.

3x + 15 -2x - 4 = 20

Simplify.

x + 11 = 20

Subtract 11 on both sides

x = 9

Your final answer is x = 9.

A man moves to lie on an island in Europe. He has a choice of two water companies: Manana Water: No standing charge. Pay £0.06 per m3 of water used.
Channel Water: Standing Charge: £30 every 3 months
£0.02 per m3 of water used
Special offer: 20% off your first bill.

he estimates that he uses 700m3 of water every 3 months. which company should he choose?

Answers

Manana would be the best choice in the long run—see all my work below.

Regular prices:

Manana: $700*.06=42$ £/3mos
Channel: $(700*.02)+30=44$ £/3mos

However, with the 20% discount on Channel Water, the first three months would look like:

(NOTE: This may be an overly complicated equation, but it's how it works out in my head.)

$((((700)/(3))2*.02)+30)-(((700*.02+30)/(100))20)=30.53$ £ for the first three months.

Manana:
$4*42=168$ £/year

Channel:
$(2.75*44)+30.53=151.53$ £ for the first year, and $4*44=176$ £/year afterwards.

if a coin and a number cube are tossed at the same time, what is the probability of tossing heads and rolling an even number

Answers

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Using the factorised trinomial $(n-2)(4n-7)$ , prove that there are only two values of n for which $4 n^(2) - 15n + 14$ is a prime number.

Answers

4n² - 15n + 14 is always the product of two numbers, for it to be prime number, one of these factors must be either 1 or -1.

Case n - 2 = 1
That would be n = 3
Then 4n² - 15n + 14 = 5 , which is prime.

Case n - 2 = -1
That would be n = 1
Then 4n² - 15n + 14 = 3, which is also prime.

Case 4n - 7 = 1
That would be n = 2 and that makes other factor (n-2) zero so it's not prime

Case 4n-7 = -1
That would be n = 3/2 which is not integer, so 4n² - 15n + 14 will not be interger.

For any other n values, 4n² - 15n + 14 will be composite number since it is product of two factors.

Therefore we are left with n = 1 and n = 3; only two values of n.

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