Maths-
General
Easy

Question

Which expression is equivalent to x to the power of 4 minus 18 x squared plus 81 ?

  1. left parenthesis x minus 3 right parenthesis to the power of 4
  2. left parenthesis x minus 3 right parenthesis left parenthesis x plus 3 right parenthesis cubed
  3. left parenthesis x minus 3 right parenthesis cubed left parenthesis x plus 3 right parenthesis
  4. left parenthesis x minus 3 right parenthesis squared left parenthesis x plus 3 right parenthesis squared

The correct answer is: left parenthesis x minus 3 right parenthesis squared left parenthesis x plus 3 right parenthesis squared


    HINT : the equation is in the form of a2 -2ab +b2  and factorize the equation further after getting in the form of (a-b)2
    Explanation:
    Step 1 :
    Factorization x to the power of 4 minus 18 x squared plus 81 equals open parentheses x squared close parentheses squared minus 2 space cross times space left parenthesis 9 right parenthesis space cross times space open parentheses x squared close parentheses plus left parenthesis 9 right parenthesis squared
    We know that a squared minus 2 a b plus b squared equals left parenthesis a minus b right parenthesis squared
    Here a equals x squared text  and  end text b equals 9
    so x to the power of 4 minus 18 x squared plus 81 equals open parentheses x squared minus 9 close parentheses squared
    Step 2:
    We can write 9 as 32 so we can divide further
    open parentheses x squared minus 9 close parentheses squared equals open parentheses x squared minus 3 squared close parentheses squared
    We know that a squared minus b squared equals left parenthesis a plus b right parenthesis left parenthesis a minus b right parenthesis
    Here a equals x text  and  end text b equals 3
    open parentheses x squared minus 3 squared close parentheses squared equals left square bracket left parenthesis x plus 3 right parenthesis left parenthesis x minus 3 right parenthesis right square bracket squared equals left parenthesis x minus 3 right parenthesis squared left parenthesis x plus 3 right parenthesis squared
    So, x to the power of 4 minus 18 x squared plus 81 equals left parenthesis x minus 3 right parenthesis squared left parenthesis x plus 3 right parenthesis squared

    Related Questions to study

    General
    Maths-


    Triangle DEF (not shown) is similar to triangle ABC above, where side DE corresponds to side AB, side DF corresponds to side AC , and DE = AB. What is the measure of angle DEF ?


    Triangle DEF (not shown) is similar to triangle ABC above, where side DE corresponds to side AB, side DF corresponds to side AC , and DE = AB. What is the measure of angle DEF ?

    Maths-General
    General
    Maths-


    The function f models Jack's pulse, in beats per minute (bpm), as a function of his speed, in kilometers per hour (km/h), on a stationary bicycle. Based on the model, what was Jack's pulse, in bpm, when his sped was 0 km/h?


    The function f models Jack's pulse, in beats per minute (bpm), as a function of his speed, in kilometers per hour (km/h), on a stationary bicycle. Based on the model, what was Jack's pulse, in bpm, when his sped was 0 km/h?

    Maths-General
    General
    Maths-

    ka + nb = 10
    The given equation relates the positive numbers a, b, k and n. Which of the following correctly expresses a in terms of b, k , and n ?

    ka + nb = 10
    The given equation relates the positive numbers a, b, k and n. Which of the following correctly expresses a in terms of b, k , and n ?

    Maths-General
    parallel
    General
    Maths-


    What system of linear equations is represented by the lines shown?


    What system of linear equations is represented by the lines shown?

    Maths-General
    General
    Maths-

    What is the x-intercept of the graph of 8x + 6y = 24 in the xy-plane?

    What is the x-intercept of the graph of 8x + 6y = 24 in the xy-plane?

    Maths-General
    General
    Maths-

    A college mathematics department plans to spend straight $1,800 buying computers and books. Each computer costs straight $300 and each book costs straight $90 . Which equation represents this situation, where x is the number of computers and y is the number of books that the department can buy?

    A college mathematics department plans to spend straight $1,800 buying computers and books. Each computer costs straight $300 and each book costs straight $90 . Which equation represents this situation, where x is the number of computers and y is the number of books that the department can buy?

    Maths-General
    parallel
    General
    Maths-

    Which of the following is equivalent to 2 open parentheses x squared minus x close parentheses plus 3 open parentheses x squared minus x close parentheses?

    Which of the following is equivalent to 2 open parentheses x squared minus x close parentheses plus 3 open parentheses x squared minus x close parentheses?

    Maths-General
    General
    Maths-

    2 x minus y equals 8
    x plus 2 y equals 4
    For the system of equations above, what is the value of x + y?

    2 x minus y equals 8
    x plus 2 y equals 4
    For the system of equations above, what is the value of x + y?

    Maths-General
    General
    General

    Ohm's law is applicable to

    • Ohm's law is not applicable for non ohmic conductors.
    • It is only true for ohmic conductors.

    Ohm's law is applicable to

    GeneralGeneral

    • Ohm's law is not applicable for non ohmic conductors.
    • It is only true for ohmic conductors.

    parallel
    General
    General

    A cinquain poem is a collection of __________.

    A cinquain poem is a collection of __________.

    GeneralGeneral
    General
    General

    Find the equation to find the total area of the given figure.

    For such questions, we should know distributive property.

    Find the equation to find the total area of the given figure.

    GeneralGeneral

    For such questions, we should know distributive property.

    General
    General

    An ice cream store can make 280 quarts of ice cream in 7 hours. ____________ quarts of ice cream can be made in 48 hours.

    We should be careful about the units. Before operation we should make sure same quantities have same unit.

    An ice cream store can make 280 quarts of ice cream in 7 hours. ____________ quarts of ice cream can be made in 48 hours.

    GeneralGeneral

    We should be careful about the units. Before operation we should make sure same quantities have same unit.

    parallel
    General
    General

    Write the equivalent expressions for the following:
    10(m + 10)

    For such questions, we should the properties required to solve algebraic expression.

    Write the equivalent expressions for the following:
    10(m + 10)

    GeneralGeneral

    For such questions, we should the properties required to solve algebraic expression.

    General
    General

    400 inch is _____% of 1600 inches.

     

    400 inch is _____% of 1600 inches.

    GeneralGeneral

     

    General
    Science

    The temperature at which a substance fuses is called its _____.

    The temperature at which a substance fuses is called its _____.

    ScienceGeneral
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.