Notice that 16t2= (4t)2 and 1= 12. There is a special formula for a "difference of two squares".Saturnfirefly said:Homework Statement
1, 2. Factorize completely:
80t^5-5t
3X-9X^2+12
solve: 3. 1/2x = 1/6+1/3X
4. A right-angle triangle has the hypotenuse 16.0, one of the short sides is 3 cm longer than the other. Area and perimeter?
Homework Equations
The Attempt at a Solution
1. 5t(16t^4-1)
That isn't "factored" at all! It is not ( )( ). You should be able to see immediately that you can factor out a 3: 3x2- 9x+ 12= 3(x2- 3x+ 4). Now can you factor 4 into two integers whose "sum" is -3?2. x(3-9x)+12 are they completely factorized though?
You mean, I think, "solve 1/(2x)= 1/6+ 1/(3x). (What you wrote could be interpreted as (1/2)x= 1/6+ (1/3)x.) You didn't really need to multiply the left side by 18: 6 would have done it. 1/6+ 1/(3x)= 1/6+ 2/(6x)= (x+ 2)/6x Any way, "cross multiplying": multiply the left by 18x and the right by 2x gives 18x= 2x2+ 4x. I find it confusing to "cross multiply". I would prefer to say "multiply both sides by the least common denominator" which is 6x: 6x(1/(2x))= 6x(1/6)+ (6x)(1/3x) so 3= x+ 2 (not what I got above- I messed up the "cross multiply"!) . Can you solve 3= x+ 2?3. I cross multiplied until I got: 18X = 5X^2 + 12X... can't get any further
A right-angle triangle has the hypotenuse 16.0, one of the short sides is 3 cm longer than the other. Area and perimeter?4. no success
HallsofIvy said:Notice that 16t2= (4t)2 and 1= 12. There is a special formula for a "difference of two squares".
That isn't "factored" at all! It is not ( )( ). You should be able to see immediately that you can factor out a 3: 3x2- 9x+ 12= 3(x2- 3x+ 4). Now can you factor 4 into two integers whose "sum" is -3?
You mean, I think, "solve 1/(2x)= 1/6+ 1/(3x). (What you wrote could be interpreted as (1/2)x= 1/6+ (1/3)x.) You didn't really need to multiply the left side by 18: 6 would have done it. 1/6+ 1/(3x)= 1/6+ 2/(6x)= (x+ 2)/6x Any way, "cross multiplying": multiply the left by 18x and the right by 2x gives 18x= 2x2+ 4x. I find it confusing to "cross multiply". I would prefer to say "multiply both sides by the least common denominator" which is 6x: 6x(1/(2x))= 6x(1/6)+ (6x)(1/3x) so 3= x+ 2 (not what I got above- I messed up the "cross multiply"!) . Can you solve 3= x+ 2?
Factorizing is the process of finding the factors, or smaller numbers that can be multiplied together to get a larger number, of a given expression or equation. This is commonly used in algebra and can help simplify complicated equations.
To factorize an equation, you need to identify the common factors between all the terms in the equation. You can then use the distributive property to rewrite the equation in a factored form. It may also be helpful to use techniques such as grouping or the difference of squares to factorize more complex equations.
Some common methods for solving equations include factoring, substitution, elimination, and graphing. Each method may be more suitable for different types of equations, so it is important to understand the strengths and weaknesses of each method.
No, not all equations can be solved using factorizing. Some equations may require more advanced methods such as quadratic formula or completing the square. It is important to understand when to use factorizing and when to use other methods for solving equations.
Factorizing can be used in various real-life situations, such as in finance to find the most efficient way to distribute money between different investments, or in biology to understand the genetic traits of offspring. It is a useful skill for problem-solving and critical thinking in many fields.