Factoring perfect square trinomials (article) | Khan Academy (2024)

Learn how to factor quadratics that have the "perfect square" form. For example, write x²+6x+9 as (x+3)².

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  • Aaishahali

    6 years agoPosted 6 years ago. Direct link to Aaishahali's post “is (4+x)^2 the same as (...”

    is (4+x)^2 the same as (x+4)^2

    (26 votes)

    • Rex Schmitz 🐉🐍

      6 years agoPosted 6 years ago. Direct link to Rex Schmitz 🐉🐍's post “Yes, they are the same, a...”

      Factoring perfect square trinomials (article) | Khan Academy (4)

      Factoring perfect square trinomials (article) | Khan Academy (5)

      Yes, they are the same, as you can switch the numbers around within the parenthesis, just not outside of them.

      (39 votes)

  • Sanjna Ayyar

    7 years agoPosted 7 years ago. Direct link to Sanjna Ayyar's post “Just curious, what's the ...”

    Just curious, what's the point of doing this to an expression? Like, where will this be applied?

    (11 votes)

  • sean cabo

    8 years agoPosted 8 years ago. Direct link to sean cabo's post “Number three marks (X+7) ...”

    Number three marks (X+7) squared wrong as well, but the "I need help" section is correct.

    (4 votes)

    • Gustavo Delazeri

      7 years agoPosted 7 years ago. Direct link to Gustavo Delazeri's post “Maybe your Caps Lock is o...”

      Factoring perfect square trinomials (article) | Khan Academy (14)

      Factoring perfect square trinomials (article) | Khan Academy (15)

      Maybe your Caps Lock is on. (X+7) is different from (x+7).
      Hope I have helped :)

      (26 votes)

  • mtchuenkam

    7 years agoPosted 7 years ago. Direct link to mtchuenkam's post “I don't understand questi...”

    I don't understand question 4 and 5. in question 4 he said ""notice that the middle term is two times the product of the numbers that are squared: 2(3x)(5)=30x2(3x})(\D 5)=30x2(3x)(5)=30x2, l, 3, x, D, 5, equals, 30, x. then he does the equation again and shows the answer I don't understand how he got there

    (7 votes)

    • Eric Parker

      7 years agoPosted 7 years ago. Direct link to Eric Parker's post “normally when you have fo...”

      Factoring perfect square trinomials (article) | Khan Academy (19)

      normally when you have for example x^2+6x+9 you would take the root of 9 and multiply it by 2. if the answer is the first-degree variable coefficient (6) then it satisfy the perfect squares "trick" rule, and the answer would be (x+3)^2.

      when you have a coefficient to the 2nd-degree variable like in 9x^2+30x+25, you do almost the same:
      first you find the root of the 0-degree variable (25), which is 5. (5^2=25)
      then you find the root of the 2nd-degree variable's coefficient (9), which is 3 (3^2=9).

      now here is the different from before: you need to multiply both roots (3 and 5) and then multiply them by 2 (as you normally would). if the answer is the same as the 1st-degree variable's coefficient ((5*3)*2=30) then the trick can be applied here also, giving you the answer made of those 2 roots you found erlier(3 and 5)-squared.
      (3x+5)^2
      hope you understood and that it helped you.

      (11 votes)

  • Ian Philbrick-Miller

    7 years agoPosted 7 years ago. Direct link to Ian Philbrick-Miller's post “What do the a and b stand...”

    What do the a and b stand for in the equation a^2+2ab+b^2 ? I'm very confused :/

    (4 votes)

    • Sans

      4 years agoPosted 4 years ago. Direct link to Sans's post “they are just any varible...”

      they are just any varibles. a and b can be anything (a has to be equal to a and b has to be equal to b tho)

      (1 vote)

  • HermioneGranger1219

    4 years agoPosted 4 years ago. Direct link to HermioneGranger1219's post “is algebra 1 a high schoo...”

    is algebra 1 a high school class because im taking it in middle school

    (3 votes)

    • KC

      4 years agoPosted 4 years ago. Direct link to KC's post “It can be, many people ta...”

      It can be, many people take algebra in middle school but there are also plenty of people who take it in high school. I think most people take geometry freshman year in high school (9th grade) but there are plenty of people who take it before or after

      (5 votes)

  • Loyalty Matters🔥❤

    9 months agoPosted 9 months ago. Direct link to Loyalty Matters🔥❤'s post “Does anyone understand th...”

    Does anyone understand this at all?

    (5 votes)

  • smitters

    a year agoPosted a year ago. Direct link to smitters's post “problem 7 doesnt have pow...”

    problem 7 doesnt have power (degree) button to write the correct answer. Need Fix

    (3 votes)

    • Kim Seidel

      a year agoPosted a year ago. Direct link to Kim Seidel's post “No fix is needed. You ca...”

      No fix is needed. You can use the ^ symbols to enter an exponent. (3x+4y)^2

      Alternatively, you can enter it as (3x+4y)(3x+4y)

      (5 votes)

  • silly goofy goober

    a year agoPosted a year ago. Direct link to silly goofy goober's post “so like do we do the stuf...”

    so like do we do the stuff we learned before or ?? what are we doing??

    (4 votes)

  • Tasha Smith

    6 months agoPosted 6 months ago. Direct link to Tasha Smith's post “For question 7, [9x^2+24x...”

    For question 7, [9x^2+24xy+16y^2]. The first and last terms are perfect squares (3x and 4y). But when I express the middle term like this, 2(3x)(4y) I got 6x8y instead of 24xy. Can someone explain?

    (2 votes)

    • Kim Seidel

      6 months agoPosted 6 months ago. Direct link to Kim Seidel's post “You have a multiplication...”

      You have a multiplication error. There is no distributive property that distributes multiplication across multiplication. The distributive property only distributes multiplication across addition or subtraction.

      To multiply 3 or more items, you do them in pairs.
      2(3x) = 6x
      6x(4y) = 24xy

      Hope this helps.

      (4 votes)

Factoring perfect square trinomials (article) | Khan Academy (2024)
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