Answer :
Let's simplify the expression [tex]\(3x^2y^5(4x^2 + 7y^4 - 5x)\)[/tex].
We'll distribute [tex]\(3x^2y^5\)[/tex] through each term in the parentheses:
1. First term: Multiply [tex]\(3x^2y^5\)[/tex] by [tex]\(4x^2\)[/tex]:
[tex]\[
3x^2y^5 \times 4x^2 = (3 \times 4)(x^{2+2})(y^5) = 12x^4y^5
\][/tex]
2. Second term: Multiply [tex]\(3x^2y^5\)[/tex] by [tex]\(7y^4\)[/tex]:
[tex]\[
3x^2y^5 \times 7y^4 = (3 \times 7)(x^2)(y^{5+4}) = 21x^2y^9
\][/tex]
3. Third term: Multiply [tex]\(3x^2y^5\)[/tex] by [tex]\(-5x\)[/tex]:
[tex]\[
3x^2y^5 \times (-5x) = (3 \times -5)(x^{2+1})(y^5) = -15x^3y^5
\][/tex]
Now, combine the results from all three terms to get the simplified expression:
[tex]\[
12x^4y^5 + 21x^2y^9 - 15x^3y^5
\][/tex]
The correct answer is B) [tex]\(12x^4y^5 + 21x^2y^9 - 15x^3y^5\)[/tex].
We'll distribute [tex]\(3x^2y^5\)[/tex] through each term in the parentheses:
1. First term: Multiply [tex]\(3x^2y^5\)[/tex] by [tex]\(4x^2\)[/tex]:
[tex]\[
3x^2y^5 \times 4x^2 = (3 \times 4)(x^{2+2})(y^5) = 12x^4y^5
\][/tex]
2. Second term: Multiply [tex]\(3x^2y^5\)[/tex] by [tex]\(7y^4\)[/tex]:
[tex]\[
3x^2y^5 \times 7y^4 = (3 \times 7)(x^2)(y^{5+4}) = 21x^2y^9
\][/tex]
3. Third term: Multiply [tex]\(3x^2y^5\)[/tex] by [tex]\(-5x\)[/tex]:
[tex]\[
3x^2y^5 \times (-5x) = (3 \times -5)(x^{2+1})(y^5) = -15x^3y^5
\][/tex]
Now, combine the results from all three terms to get the simplified expression:
[tex]\[
12x^4y^5 + 21x^2y^9 - 15x^3y^5
\][/tex]
The correct answer is B) [tex]\(12x^4y^5 + 21x^2y^9 - 15x^3y^5\)[/tex].
