High School

Rewrite without parentheses and simplify as much as possible:

[tex] -4x^3y(3x^6 - 9x^4y^5 + 7y^5) [/tex]

Answer :

Sure, let's simplify the expression step-by-step:

We start with the expression:

[tex]\[
-4x^3y(3x^6 - 9x^4y^5 + 7y^5)
\][/tex]

We'll use the distributive property to remove the parentheses by multiplying [tex]\(-4x^3y\)[/tex] with each term inside the parentheses separately.

1. Multiply [tex]\(-4x^3y\)[/tex] by [tex]\(3x^6\)[/tex]:

[tex]\[
-4x^3y \cdot 3x^6 = -12x^{3+6}y = -12x^9y
\][/tex]

2. Multiply [tex]\(-4x^3y\)[/tex] by [tex]\(-9x^4y^5\)[/tex]:

[tex]\[
-4x^3y \cdot (-9x^4y^5) = 36x^{3+4}y^{1+5} = 36x^7y^6
\][/tex]

3. Multiply [tex]\(-4x^3y\)[/tex] by [tex]\(7y^5\)[/tex]:

[tex]\[
-4x^3y \cdot 7y^5 = -28x^3y^{1+5} = -28x^3y^6
\][/tex]

Now, we combine all the terms:

[tex]\[
-12x^9y + 36x^7y^6 - 28x^3y^6
\][/tex]

This is the simplified expression without parentheses. Each term is simplified by adding the exponents for the same variables. Let me know if you have any questions!