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Answer :
Let's simplify the expression step-by-step:
Expression to simplify:
[tex]\[ 9x^4 y^5(-5x^3 y^3 - 3y^3) \][/tex]
Step 1: Distribute the terms using the distributive property.
We will distribute [tex]\( 9x^4 y^5 \)[/tex] to each term inside the parentheses.
- First term:
[tex]\[ 9x^4 y^5 \times (-5x^3 y^3) \][/tex]
Multiply the coefficients:
[tex]\[ 9 \times (-5) = -45 \][/tex]
Add the exponents of [tex]\(x\)[/tex]:
[tex]\[ x^{4+3} = x^7 \][/tex]
Add the exponents of [tex]\(y\)[/tex]:
[tex]\[ y^{5+3} = y^8 \][/tex]
So the first term becomes:
[tex]\[ -45x^7 y^8 \][/tex]
- Second term:
[tex]\[ 9x^4 y^5 \times (-3y^3) \][/tex]
Multiply the coefficients:
[tex]\[ 9 \times (-3) = -27 \][/tex]
The exponent of [tex]\(x\)[/tex] remains the same because there is no [tex]\(x\)[/tex] in [tex]\(-3y^3\)[/tex]:
[tex]\[ x^4 \][/tex]
Add the exponents of [tex]\(y\)[/tex]:
[tex]\[ y^{5+3} = y^8 \][/tex]
So the second term becomes:
[tex]\[ -27x^4 y^8 \][/tex]
Step 2: Combine the results.
Putting it all together, the expression simplifies to:
[tex]\[ -45x^7 y^8 - 27x^4 y^8 \][/tex]
Therefore, the correct answer is:
d. [tex]\(-45x^7 y^8 - 27x^4 y^8\)[/tex]
Expression to simplify:
[tex]\[ 9x^4 y^5(-5x^3 y^3 - 3y^3) \][/tex]
Step 1: Distribute the terms using the distributive property.
We will distribute [tex]\( 9x^4 y^5 \)[/tex] to each term inside the parentheses.
- First term:
[tex]\[ 9x^4 y^5 \times (-5x^3 y^3) \][/tex]
Multiply the coefficients:
[tex]\[ 9 \times (-5) = -45 \][/tex]
Add the exponents of [tex]\(x\)[/tex]:
[tex]\[ x^{4+3} = x^7 \][/tex]
Add the exponents of [tex]\(y\)[/tex]:
[tex]\[ y^{5+3} = y^8 \][/tex]
So the first term becomes:
[tex]\[ -45x^7 y^8 \][/tex]
- Second term:
[tex]\[ 9x^4 y^5 \times (-3y^3) \][/tex]
Multiply the coefficients:
[tex]\[ 9 \times (-3) = -27 \][/tex]
The exponent of [tex]\(x\)[/tex] remains the same because there is no [tex]\(x\)[/tex] in [tex]\(-3y^3\)[/tex]:
[tex]\[ x^4 \][/tex]
Add the exponents of [tex]\(y\)[/tex]:
[tex]\[ y^{5+3} = y^8 \][/tex]
So the second term becomes:
[tex]\[ -27x^4 y^8 \][/tex]
Step 2: Combine the results.
Putting it all together, the expression simplifies to:
[tex]\[ -45x^7 y^8 - 27x^4 y^8 \][/tex]
Therefore, the correct answer is:
d. [tex]\(-45x^7 y^8 - 27x^4 y^8\)[/tex]
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