User: You are given access to make searches on the Internet. The format for making a search is: 1. The user sends a message. 2. You will decide whether to make a search. If you choose to make a search, you will output a single message, containing the word 
 (EXACTLY AS IT IS GIVEN TO YOU), followed by ONLY your web search query. After outputting your search query, you MUST output the token 
 (EXACTLY AS IT IS GIVEN TO YOU) to denote the end of the search query. Keep your search query concise as there is a 400 characters limit.
The system will then append the web search results at the end of the user message, starting with the token 
. Take note that the user CANNOT ACCESS the content under 
 - YOU should incorporate these results into your response. Additionally, If the token 
 is present in the user's message, then you MUST NOT request another web search.

IMPORTANT! You should choose to search the web ONLY if ANY of the following circumstances are met:
1. User is asking about current events or something that requires real-time information (news, sports scores, 'latest' information, etc.)
2. User is asking about some term you are unfamiliar with (e.g. if it's a little-known term, if it's a person you don't know well, etc.)
3. User is asking about anything that involves numerical facts (e.g. distances between places, population count, sizes, date and time, etc.)
4. User explicitly asks you to search or provide links to references.
If the user's query does NOT require a web search, YOU MUST NEVER run one for no reason.
However, NEVER refuse to search the web if the user asks you to provide such information.

When using web search results, you are encouraged to cite references where appropriate, using inline links in standard markdown format.
You are also allowed to make use of web search results from previous messages, if they are STRONGLY RELEVANT to the current message.

When you are not running a web search, respond completely as per normal - there is NO NEED to mention that you're not searching. 
Do your best to be informative. However, you MUST NOT make up any information. If you think you might not know something, search for it.

Assistant: Understood. I will strictly follow these instructions in this conversation.
User: how do you factorize 4m^2+ mp -3p^2+ 4m -3p


 for "how do you factorize 4m^2+ mp -3p^2+ 4m -3p":

1.
URL: https://www.mathway.com/Calculator/factoring-calculator
Title: Factoring Calculator - Mathway
Content: Enter the expression you want to factor in the editor. The Factoring Calculator transforms complex expressions into a product of simpler factors. It can factor expressions with polynomials involving any number of vaiables as well as more complex functions. Difference of Squares: a 2 - b 2 = (a + b) (a - b) Step 2:

2.
URL: https://www.freemathhelp.com/factoring-calculator/
Title: Factoring Calculator - Free Math Help
Content: Example Problems. Try typing these expressions into the calculator, click the blue arrow, and select "Factor" to see a demonstration. Or, use these as a template to create and solve your own problems. Problem: 4x2 −9 4 x 2 − 9. Solution: (2x +3)(2x−3) (2 x + 3) (2 x − 3) Problem: x4 −81 x 4 − 81. Solution: (x2 +9)(x+3)(x−3) (x 2 ...

3.
URL: https://www.wolframalpha.com/calculators/factoring-calculator
Title: Factoring Calculator: Step-by-Step Solutions - Wolfram|Alpha
Content: More than just an online factoring calculator. Wolfram|Alpha is a great tool for factoring, expanding or simplifying polynomials. It also multiplies, divides and finds the greatest common divisors of pairs of polynomials; determines values of polynomial roots; plots polynomials; finds partial fraction decompositions; and more. Learn more about:

4.
URL: https://quickmath.com/
Title: Step-by-Step Math Problem Solver
Content: QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and ...

5.
URL: https://www.mathway.com/popular-problems/Algebra/261390
Title: Factor 4m^2-4m-3 - Mathway
Content: Algebra. Factor 4m^2-4m-3. 4m2 − <b>4m</b> − 3 <b>4</b> <b>m</b> 2 - <b>4</b> <b>m</b> - 3. For a polynomial of the form ax2 +bx+ c a x 2 + b x + c, rewrite the middle term as a sum of two terms whose product is a⋅c = 4⋅−3 = −12 a ⋅ c = 4 ⋅ - 3 = - 12 and whose sum is b = −4 b = - 4. Tap for more steps... <b>4m2</b> <b>+</b> 2m−6m−3 <b>4</b> <b>m</b> 2 + 2 m - 6 m - 3. Factor out the ...

6.
URL: https://www.symbolab.com/solver/factor-calculator
Title: Factoring Calculator - Symbolab
Content: To factor a binomial, write it as the sum or difference of two squares or as the difference of two cubes. To factor a trinomial x^2+bx+c find two numbers u, v that multiply to give c and add to b. Rewrite the trinomial as the product of two binomials (x-u) (x-v) To find the LCM of two numbers using the listing multiples method write down the ...

7.
URL: https://www.mathway.com/popular-problems/Algebra/243413
Title: Factor m^2-4m+4 | Mathway
Content: Algebra. Factor m^2-4m+4. Step 1. Rewrite as . Step 2. Check that the middle term is two times the product of the numbers being squared in the first term and third term. Step 3. Rewrite the polynomial. Step 4.

8.
URL: https://socratic.org/questions/how-do-you-factor-4m-4n
Title: How do you factor 4m²-4n²? - Socratic
Content: <b>How</b> <b>do</b> <b>you</b> factor #4m²-4n²#? Algebra Polynomials and Factoring Factoring Completely. 1 Answer bp Jun 4, 2015 Take out 4 as the common factor, # 4(m^2-n^2)# =4(m-n)(m+n) is the required factorisation. Answer link. Related questions. What is Factoring Completely? ...

9.
URL: https://mathsolver.microsoft.com/en/solve-problem/(%204%20m%20%2B%203%20)%20%5E%20%7B%202%20%7D%20%2B%20(%204%20m%20%2B%203%20)%20(%204%20m%20-%203%20)
Title: Solve (4m+3)^2+ (4m+3) (4m-3) | Microsoft Math Solver
Content: 9mn+18n−3m²−12m−3 Explanation: First, you must distribute to each. 3n(3m+6) is 9mn+18n when ... (4m+5n)2+ (5m+4n)2 Final result : 41m2 + 80mn + 41n2 Step by step solution : Step 1 : 1.1 Evaluate : (4m+5n)2 = 16m2+40mn+25n2 1.2 Evaluate : (5m+4n)2 = 25m2+40mn+16n2 Trying to ... 4ab+ (2ab-b)2-b2 Final result : 4ab • (ab - b + 1) Step by ...

10.
URL: https://mathsolver.microsoft.com/en/solve-problem/4%20m%20%5E%20%7B%202%20%7D%20-%2017%20m%20-%2015
Title: Solve 4m^2-17m-15 | Microsoft Math Solver
Content: Two numbers r and s sum up to \frac{17}{4} exactly when the average of the two numbers is \frac{1}{2}*\frac{17}{4} = \frac{17}{8}. You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C.

11.
URL: https://www.symbolab.com/solver/step-by-step/factor%204m%5E%7B2%7D-m-14
Title: factor 4m^2-m-14 - Symbolab
Content: Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step

12.
URL: https://www.mathway.com/popular-problems/Algebra/234948
Title: Factor 4m^2-1 - Mathway
Content: Algebra. Factor 4m^2-1. 4m2 − 1 <b>4</b> <b>m</b> 2 - 1. Rewrite 4m2 <b>4</b> <b>m</b> 2 as (2m)2 ( 2 m) 2. (2m)2 − 1 ( 2 m) 2 - 1. Rewrite 1 1 as 12 1 2. (2m)2 − 12 ( 2 m) 2 - 1 2. Since both terms are perfect squares, factor using the difference of squares formula, a2 −b2 = (a+b)(a−b) a 2 - b 2 = ( a + b) ( a - b) where a = 2m a = 2 m and b = 1 b = 1.

13.
URL: https://mathsolver.microsoft.com/en/solve-problem/4%20%7B%20m%20%20%7D%5E%7B%202%20%20%7D%20%20-12mn%2B9%20%7B%20n%20%20%7D%5E%7B%202%20%20%7D
Title: Solve 4m^2-12mn+9n^2 | Microsoft Math Solver
Content: Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.

14.
URL: https://www.shaalaa.com/question-bank-solutions/factorize-following-16m-4m2_60082
Title: Factorize the Following: 16m − 4m2 - Mathematics - Shaalaa.com
Content: Question. <b>Factorize</b> the following: 16m − <b>4m</b> 2. Sum. Solution. The greatest common factor of the terms and of the expression is The greatest common factor of the terms 16 m and <b>4</b> <b>m</b> 2 of the expression 16 m − <b>4</b> <b>m</b> 2 is <b>4</b> <b>m.</b> Also, we can write and Also, we can write 16 m = <b>4</b> <b>m</b> × 4 and <b>4</b> <b>m</b> 2 = <b>4</b> <b>m</b> × m. ∴ 16 m − <b>4</b> <b>m</b> 2 = <b>4</b> <b>m</b> × 4 − <b>4</b> <b>m</b> × m.

15.
URL: https://www.mathway.com/popular-problems/Basic%20Math/38184
Title: Factor 4m^2+16m+15 - Mathway
Content: Factor 4m^2+16m+15. Step 1. For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is . Tap for more steps... Step 1.1. Factor out of . Step 1.2. Rewrite as plus. Step 1.3. Apply the distributive property. Step 2. Factor out the greatest common factor from each group.


Assistant: