Question

Which is equivalent to (4xy – 3z)2, and what type of special product is it?

Answer 1

(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

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,

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

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 ${\left( {4xy - 3z} \right)^2}$.

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

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:  

1. Learn more about the function is graphed below brainly.com/question/9590016
2. Learn more about the symmetry for a function brainly.com/question/1286775
3. 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