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3 years ago

Simplify the following expression (-5x + 6x2) - (6x2 – 5x)

Mathematics

2 answers:

Nookie1986 [14]3 years ago

5 0

Answer:

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Distributive Property

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

(-5x + 6x²) - (6x² - 5x)

Step 2: Simplify

[Distributive Property] Distribute negative: -5x + 6x² - 6x² + 5x
[Subtraction] Combine like terms (x²): -5x + 5x
[Addition] Combine like terms (x): 0

netineya [11]3 years ago

5 0

Answer:

❊ $\large{ \tt{STEP - BY - STEP \: EXPLANATION}} :$

♡ Firstly , Here are some of the questions & their answers which should be known before simplifying the given expression :

Q. Do I have to change the sign of each term of second expression while subtracting ?

Ans : Yep! While subtracting , sign of each term of the second expression changes whereas In addition , sign of each term in the expressions remains unchanged.

Q. What do you mean by Like terms & Unlike terms ?

Ans : Well , Like terms are those which have the same base whereas Unlike terms are those which have the different base [ For eg : In 4x , 2y , 3x & 4y , 4x & 3x are like terms and 2y and 4y are like terms ]. Also Remember : Only coefficients of like terms can be added or subtracted.

The Question / Answer part ends up here. Now , Let's get started for simplifying the given expression :

$\large{ \bf{❊ \: ( - 5 {x}^{} + 6 {x}^{2} ) - (6 {x }^{2} - 5x)}}$

$\large{ \bf{ ↬ \: - 5x + 6 {x}^{2} - 6 {x}^{2} + 5x}}$

$\large{ \bf{↬ - 5x + 5x + 6 {x}^{2} - 6 {x}^{2} }}$

-Here , We can see the like terms with different signs. So, they cancel out each other.

$\large{ \bf{↬ \: \cancel{5x} + \cancel{5x}} + \cancel{6 {x}^{2}} - \cancel{6 {x}}^{2} }$

-We're left with nothing , So the answer would be ' 0 ' .

$\boxed{ \large{ \bf{↬0}}}$

$\boxed{ \boxed {\large{ \tt{⟿ \: OUR\: FINAL \: ANSWER : \boxed{ \underline{ \bf{0}}}}}}}$

✺ Don't Give Up , The Beginning Is Always The Hardest! ♪

❃ Hope I helped! ツ

☃ Have a wonderful day / evening ! ☼

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How many integers between 10 and 60, inclusive, can be evenly divided by neither 2 nor 3?

erastovalidia [21]

Find total number of integers.

$a_1=10,a_n=60,d=1 \\a_n=a_1+(n-1)d \\60=10+(n-1)1 \\n-1=50 \\n=51$

Find how many integers is divisible by 2.

$a_1=10,a_n=60,d=2
\\a_n=a_1+(n-1)d
\\60=10+(n-1)2
\\2(n-1)=50
\\n-1=25
\\n=26$

Eliminate even numbers.

11, 13, 15,..., 57, 59

This array contains 51 - 26 = 25 numbers.

Eliminate numbers before the first number divisible by 3 and after the last number divisible by 3.

15, 17, 19,..., 55, 57

This array contains 25 - 3 = 22 numbers.

Now we should eliminate numbers divisible by 3: 15, 21, 27...

$a_1=15,a_n=57,d=6,n=?
\\a_n=a_1+(n-1)d
\\57=15+(n-1)6
\\6(n-1)=42
\\n-1=7
\\n=8$

There are 8 such numbers.

Therefore, there are 25 - 8 = 17 numbers that can be evenly divided by neither 2 nor 3

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3 years ago

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Ulleksa [173]

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3 years ago

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Amanda [17]

Answer:

2nd - (w - 5)(w + 5)

4th - (-4v - 9)(-4v + 9)

Step-by-step explanation:

1. The first option shows an expression multiplied by its opposite(x -1), so therefore, it does not show the difference of squares

2. The second option does show the difference of squares because it is in the form (a + b)(a - b)

3. The third option is just a square because the same expression is multiplied by itself.

4. The fourth option is the difference of squares because it is in the form (a + b)(a - b). a equals -4v and b equals 9 in this case.

5. The fifth option is not the difference of squares. No term in common in both expressions

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