Question

lesson 18.1 checkpoint□ once you have completed the above problems and checked your solutions, complete the lesson checkpoint below.□ complete the lesson reflection above by circling your current understanding of the learning goal.find each product. simplify as much as possible.1. $7xy(3x^{2}y^{3})$2. $(6xyz^{4})(5xy^{3})$3. $(x^{3}+2x^{2})x^{4}$4. $6xy^{2}(x^{4}+3x^{3}y+3xy^{3})$

Explanation:

Step1: Multiply coefficients, add exponents

$7xy(3x^2y^3) = (7 \times 3)x^{1+2}y^{1+3}$

Step2: Simplify the expression

$= 21x^3y^4$

Step1: Multiply coefficients, add exponents

$(6xyz^4)(5xy^3) = (6 \times 5)x^{1+1}y^{1+3}z^4$

Step2: Simplify the expression

$= 30x^2y^4z^4$

Step1: Distribute $x^4$ to each term

$(x^3 + 2x^2)x^4 = x^3 \cdot x^4 + 2x^2 \cdot x^4$

Step2: Add exponents for each term

$= x^{3+4} + 2x^{2+4}$

Step3: Simplify the expression

$= x^7 + 2x^6$

Step1: Distribute $6xy^2$ to each term

$6xy^2(x^4 + 3x^3y + 3xy^3) = 6xy^2 \cdot x^4 + 6xy^2 \cdot 3x^3y + 6xy^2 \cdot 3xy^3$

Step2: Multiply coefficients, add exponents

$= 6x^{1+4}y^2 + 18x^{1+3}y^{2+1} + 18x^{1+1}y^{2+3}$

Step3: Simplify each term

$= 6x^5y^2 + 18x^4y^3 + 18x^2y^5$

Answer:

1. $21x^3y^4$
2. $30x^2y^4z^4$
3. $x^7 + 2x^6$
4. $6x^5y^2 + 18x^4y^3 + 18x^2y^5$