Question

multiply.
1
$-14x^{2}(3x^{3}y^{4})$
2
$5x^{2}(7x^{7}y^{5})$
3
$9x^{2}y(x^{3}y^{2})$
4
$-9x^{2}y^{9}(-10x^{3}y^{5})$

Explanation:

Problem 1: $-14x^2(3x^3y^4)$

Step1: Multiply coefficients

Multiply -14 and 3: $-14\times3 = -42$

Step2: Multiply $x$ terms

Use exponent rule $a^m\times a^n = a^{m + n}$ for $x^2\times x^3$: $x^{2+3}=x^5$

Step3: Keep $y$ term

The $y^4$ remains as is.

Step4: Combine all parts

Combine the coefficient, $x$ term, and $y$ term: $-42x^5y^4$

Step1: Multiply coefficients

Multiply 5 and 7: $5\times7 = 35$

Step2: Multiply $x$ terms

Use exponent rule for $x^2\times x^7$: $x^{2 + 7}=x^9$

Step3: Keep $y$ term

The $y^5$ remains as is.

Step4: Combine all parts

Combine the coefficient, $x$ term, and $y$ term: $35x^9y^5$

Step1: Multiply coefficients

The coefficient of the second term is 1 (implied), so $9\times1 = 9$

Step2: Multiply $x$ terms

Use exponent rule for $x^2\times x^3$: $x^{2+3}=x^5$

Step3: Multiply $y$ terms

Use exponent rule for $y^1\times y^2$ (since $y = y^1$): $y^{1 + 2}=y^3$

Step4: Combine all parts

Combine the coefficient, $x$ term, and $y$ term: $9x^5y^3$

Answer:

$-42x^5y^4$

Problem 2: $5x^2(7x^7y^5)$