Question

evaluate independent practice
lesson 18.1 homework
□ complete problems 1 - 8 for independent practice.
when you are finished, check the solutions with your teacher.
find each product.

1. $(4xy)(5x^{2}y^{2})$
2. $11(2x + 3x^{2})$
3. $(15z^{3}+5z)3x^{2}z$
4. $(6m^{2}n^{2})(4m^{4}n^{3})$

simplify

1. $3(x - 2)-(x^{2}-5)$
2. $6(x^{2}+3x)+(x^{2}+3x + 2)$

find each product.

1. $(c + 2d)(2c)?$
2. $(2x^{2}+3xy)(4x^{2})?$

optional: complete problems 3-4,7-9,11-14 from your textbook on separate lined paper.
when you are finished, check the solutions at the back of the textbook.

Explanation:

Step1: Multiply coefficients, add exponents

$(4xy)(5x^2y^2) = (4 \times 5)x^{1+2}y^{1+2}$
$= 20x^3y^3$

Step2: Distribute the 11 to each term

$11(2x + 3x^2) = 11 \times 2x + 11 \times 3x^2$
$= 22x + 33x^2$

Step3: Distribute $3x^2z$ to each term

$(15z^3 + 5z)3x^2z = 15z^3 \times 3x^2z + 5z \times 3x^2z$
$= 45x^2z^4 + 15x^2z^2$

Step4: Multiply coefficients, add exponents

$(6m^2n^2)(4m^4n^3) = (6 \times 4)m^{2+4}n^{2+3}$
$= 24m^6n^5$

Step5: Distribute and combine like terms

$3(x - 2) - (x^2 - 5) = 3x - 6 - x^2 + 5$
$= -x^2 + 3x - 1$

Step6: Distribute and combine like terms

$6(x^2 + 3x) + (x^2 + 3x + 2) = 6x^2 + 18x + x^2 + 3x + 2$
$= 7x^2 + 21x + 2$

Step7: Distribute $2c$ to each term

$(c + 2d)(2c) = c \times 2c + 2d \times 2c$
$= 2c^2 + 4cd$

Step8: Distribute $4x^2$ to each term

$(2x^2 + 3xy)(4x^2) = 2x^2 \times 4x^2 + 3xy \times 4x^2$
$= 8x^4 + 12x^3y$

Answer:

1. $20x^3y^3$
2. $33x^2 + 22x$
3. $45x^2z^4 + 15x^2z^2$
4. $24m^6n^5$
5. $-x^2 + 3x - 1$
6. $7x^2 + 21x + 2$
7. $2c^2 + 4cd$
8. $8x^4 + 12x^3y$