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3 years ago

How to factor 8x^3-216

Mathematics

2 answers:

Alex777 [14]3 years ago

8 0

$8x^3-216\to\boxed{8(x^3-27)}$

lara [203]3 years ago

3 0

$8x^3-216=\left(2x\right)^3-6^3=(*)\\--------------------------\\use:a^3-b^3=(a-b)(a^2+ab+b^2)\\--------------------------\\\\(*)=(2x-6)[(2x)^2+2x\times6+6^2]=\boxed{(2x-6)(4x^2+12x+36)}\\\\========================================$

$Other:\\\\8x^3-216=8(x^3-27)=8(x^3-3^3)=8(x-3)(x^2-3x+3^2)\\\\=\boxed{8(x-3)(x^2-3x+9)}$

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Drag the tiles to the boxes to form correct pairs. Match the pairs of equivalent expressions.

Rashid [163]

Answer:

The following pairs/results are matched:

$5\left(2t+1\right)+\left(-7t+28\right)$ = $3t+33$
$3\left(3t-4\right)-\left(2t+10\right)$ = $7t-22$

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$ = $\frac{16t}{3}-\frac{23}{5}$

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$ = $-\frac{11}{4}t+36$

Step-by-step explanation:

Lets solve all the expressions to match the results.

$5\left(2t+1\right)+\left(-7t+28\right)$

Solving the expression

$5\left(2t+1\right)+\left(-7t+28\right)$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$5\left(2t+1\right)-7t+28$

$10t+5-7t+28$

$3t+33$

Therefore, $5\left(2t+1\right)+\left(-7t+28\right)$ = $3t+33$

$3\left(3t-4\right)-\left(2t+10\right)$

Solving the expression

$3\left(3t-4\right)-\left(2t+10\right)$

$9t-12-\left(2t+10\right)$

$9t-12-2t-10$

$7t-22$

Therefore, $3\left(3t-4\right)-\left(2t+10\right)$ = $7t-22$

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$

Solving the expression

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$4t-\frac{8}{5}-\left(3-\frac{4}{3}t\right)$

$4t-\frac{8}{5}-\left(-\frac{4t}{3}+3\right)$

$4t-\frac{8}{5}-3+\frac{4t}{3}$

$-3-\frac{8}{5}:\quad -\frac{23}{5}$ and $\frac{4t}{3}+4t:\quad \frac{16t}{3}$

So,

$4t-\frac{8}{5}-3+\frac{4t}{3}$ will become $\frac{16t}{3}-\frac{23}{5}$

Therefore, $\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$ = $\frac{16t}{3}-\frac{23}{5}$

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$

Solving the expression

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$-\frac{9}{2}t+3+\frac{7}{4}t+33$

$\mathrm{Group\:like\:terms}$

$\frac{9}{2}t+\frac{7}{4}t+3+33$

$\mathrm{Add\:similar\:elements:}\:-\frac{9}{2}t+\frac{7}{4}t=-\frac{11}{4}t$

$-\frac{11}{4}t+3+33$

$-\frac{11}{4}t+36$

Therefore, $\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$ = $-\frac{11}{4}t+36$

Thus, the following pairs/results are matched:

$5\left(2t+1\right)+\left(-7t+28\right)$ = $3t+33$
$3\left(3t-4\right)-\left(2t+10\right)$ = $7t-22$

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$ = $\frac{16t}{3}-\frac{23}{5}$

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$ = $-\frac{11}{4}t+36$

Keywords: algebraic expression

Learn more about algebraic expression from brainly.com/question/11336599

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3 years ago

Read 2 more answers

The side of a square measures (2x − 5) units. Part A: What is the expression that represents the area of the square? Show your w

kolbaska11 [484]

A. The area of a square is given as:

A = s^2

Where s is a measure of a side of a square. s = (2 x – 5) therefore,

A = (2 x – 5)^2

Expanding,

A = 4 x^2 – 20 x + 25

B. The degree of a polynomial is the highest exponent of the variable x, in this case 2. Therefore the expression obtained in part A is of 2nd degree.

Furthermore, polynomials are classified according to the number of terms in the expression. There are 3 terms in the expression therefore it is classified as a trinomial.

C. The closure property demonstrates that during multiplication or division, the coefficients and power of the variables are affected while during multiplication or division, only the coefficients are affected while the power remain the same.

5 0

3 years ago

Please hurry I have to do it in 2 minutes

elena55 [62]

Answer:

$w-0.15 = 0.25$

Step-by-step explanation:

6 0

2 years ago

How many equal sections divide a directed line segment if it is to be partitiioned with a 7:10 ratio?

Sphinxa [80]

Im Not Sure But Im Thinking 7/10 Wrote As in A Fraction .

8 0

3 years ago

Find a1 and d for an arithmetic sequence with these terms. a3=-8 and a7=32

Arte-miy333 [17]

We know that
the formula for the arithmetic sequence is
an = a1 + (n - 1)*d
where
a1 is the first term
n is the numbers of terms

for n=3 a3=-8
-8=a1+(3-1)*d-----> -8=a1+2*d-----> equation 1

for n=7 a7=32
-32=a1+(7-1)*d----> -32=a1+6*d----> equation 2

multiply equation 2 by -1-----> 32=-a1-6*d------> equation 3

add equation 1 and equation 3
-8=a1+2*d
32=-a1-6*d
----------------
24=-4*d------> d=-6
-8=a1+2*(-6) (substitute the value of d in equation 1)
-8=a1-12-----> a1=-8+12-----> a1=4

the answer is
a1=4
d=-6

4 0

3 years ago