Question

in 8 - 11, apply the properties of operations to multiply.

1. $\frac{1}{8}xcdot\frac{-4}{5}x$

$=\frac{1}{2}cdot\frac{- 2}{5}cdot xcdot x$
$=\frac{-1}{5}x^{2}$

1. $(y - 1.1)(-3y)$

$=(y)(-3y)+(-1.1)(-3y)$
$=-3y^{2}+3.3y$

1. $(1.1 - 2.7k)(-3.5k)=(-3.5k)(1.1 - 2.7k)$

$=-3.85k + 9.45k^{2}$

1. $\frac{1}{8}w(-1 + w)$

$=-\frac{1}{8}w+\frac{1}{8}w^{2}$
in 12 - 19, use the properties of operations to multiply.

1. $(9.1x)(8x)=72.8x^{2}$
2. $(-\frac{10}{5}f - 1)(-\frac{5}{10}f)$
3. $(1+\frac{3}{4}c)(\frac{4}{3}c)=\frac{4}{3}c + c^{2}$
4. $(-5.23x)(x + 1.7)=-5.23x^{2}-8.891x$
5. $(13b + 11 - 2b)(-\frac{13}{11}b)=-13b^{2}-\frac{143}{11}b$
6. $(m + m)(7.5m)=15m^{2}$

check for reasonableness paola says that when you apply the distributive property to $(2i + 7)$ and $(-5i)$, the result will have

1. what is the area of this tile?

Explanation:

Step1: Multiply coefficients and variables separately

For $\frac{1}{8}x\cdot\frac{- 4}{5}x$, we first multiply the coefficients $\frac{1}{8}$ and $\frac{-4}{5}$, and then multiply the $x$ - terms. $\frac{1}{8}\times\frac{-4}{5}=\frac{1\times(-4)}{8\times5}=\frac{-4}{40}=-\frac{1}{10}$, and $x\cdot x = x^{2}$. So $\frac{1}{8}x\cdot\frac{-4}{5}x=-\frac{1}{10}x^{2}$.

Step2: Expand $(y - 1.1)(-3y)$ using distributive property

$(y-1.1)(-3y)=y\times(-3y)-1.1\times(-3y)=-3y^{2}+3.3y$.

Step3: Expand $(1.1 - 2.7k)(-3.5k)$ using distributive property

$(1.1 - 2.7k)(-3.5k)=1.1\times(-3.5k)-2.7k\times(-3.5k)=-3.85k + 9.45k^{2}$.

Step4: Expand $\frac{1}{8}w(-1 + w)$ using distributive property

$\frac{1}{8}w(-1 + w)=\frac{1}{8}w\times(-1)+\frac{1}{8}w\times w=-\frac{1}{8}w+\frac{1}{8}w^{2}$.

Step5: Multiply $(9.1x)(8x)$

$(9.1x)(8x)=(9.1\times8)x^{2}=72.8x^{2}$.

Step6: Expand $(-\frac{10}{5}f - 1)(-\frac{5}{10}f)$

First simplify $-\frac{10}{5}=-2$ and $-\frac{5}{10}=-\frac{1}{2}$. Then $(-2f - 1)(-\frac{1}{2}f)=(-2f)\times(-\frac{1}{2}f)-1\times(-\frac{1}{2}f)=f^{2}+\frac{1}{2}f$.

Step7: Expand $(1+\frac{3}{4}c)(\frac{4}{3}c)$

$(1+\frac{3}{4}c)(\frac{4}{3}c)=1\times\frac{4}{3}c+\frac{3}{4}c\times\frac{4}{3}c=\frac{4}{3}c + c^{2}$.

Step8: Expand $(-5.23x)(x + 1.7)$

$(-5.23x)(x + 1.7)=(-5.23x)\times x+(-5.23x)\times1.7=-5.23x^{2}-8.891x$.

Step9: Expand $(9.4a)(-4.9a - 0.5 + 1)$

$(9.4a)(-4.9a - 0.5 + 1)=(9.4a)(-4.9a + 0.5)=9.4a\times(-4.9a)+9.4a\times0.5=-46.06a^{2}+4.7a$.

Step10: Expand $(13b + 11-2b)(-\frac{13}{11}b)$

First simplify $13b + 11-2b = 11b + 11$. Then $(11b + 11)(-\frac{13}{11}b)=11b\times(-\frac{13}{11}b)+11\times(-\frac{13}{11}b)=-13b^{2}-13b$.

Step11: Expand $(m + m)(7.5m)$

Since $m + m = 2m$, then $(2m)(7.5m)=(2\times7.5)m^{2}=15m^{2}$.

Answer:

1. $-\frac{1}{10}x^{2}$
2. $-3y^{2}+3.3y$
3. $-3.85k + 9.45k^{2}$
4. $-\frac{1}{8}w+\frac{1}{8}w^{2}$
5. $72.8x^{2}$
6. $f^{2}+\frac{1}{2}f$
7. $\frac{4}{3}c + c^{2}$
8. $-5.23x^{2}-8.891x$
9. $-46.06a^{2}+4.7a$
10. $-13b^{2}-13b$
11. (No 18 - numbered problem in the clear - view part)
12. $15m^{2}$