# TSI Math: Factoring a Multivariable Trinomial

Factor completely.

3x² + 4xy – 4y²

Intermediate Algebra and Functions | Expressions, Equations, and Functions Involving Powers, Roots, and Radicals |

Mathematics and Statistics Assessment | Powers, Roots, and Radicals |

Product Type | TSI |

TSI | Mathematics and Statistics Assessment TSI Math TSI Mathematics |

TSI Math | Intermediate Algebra and Functions |

TSI Mathematics | Intermediate Algebra and Functions |

Test Prep | TSI |

### Transcript

elusive as the multi variant Try no meal That's what

that thing is face the ferocious creature by attacking the

variables first Well the x squared the y squared terms

break into their individual factors of x times x and

white times Why Pretty easily there right Well placing the

variables in the first and last terms And each binomial

naturally creates the x y term in the middle of

the tri no meal while unlike the heads of the

infamous greek hydra the regrown variables of this flavour Good

Okay last term is negative so that by no meals

must have opposite signs Okay so see this is minus

and that's a plus thinking Yeah well the coefficients of

the tri no meal or handled as usual The first

coefficient is a prime and has only two factors One

and three in the last coefficient for their has factor

Pairs of one and four in two and two Right

Well start With little trial and error to find the

right combo here nobody gets this right off the bat

usually and let's try on all three Acts and money's

4 times x plus y is that work Well Is

the proposed factor pair valiant enough to pass the first

trial Well it's multiply the binomial tze and find out

so we got three exponents for why'd times x plus

y so inside and an outside then we had the

middle Remember how all that works so let's Think about

this gives us three acts times quantity x plus y

minus for why Tens quantity x plus y we've got

three x squared plus three x y bonnie's for x

y minus four y squared and yeah that gets us

three expert minus x y monies for y squared b

there that one's close but it's not quite right Switching

the signs makes the middle term positive See the positive

one there and switching the placement of the four and

the one makes the middle term too large We can't

do that So strategy change Send the factor pair two

times two in the battle instead So what we have

here Well Let's see we've got dead this x and

that's Why i'm thinking all right so we got three

explaining to why times x plus two why and that

pull out the three x there and that gets us

x plus two y minus two times exposed to why

and then the factors there Three x squared plus six

wide minus two Excellent on movements that kid says three

x squared plus for x y minus four y squared

Yeah there we go make like hercules and be proud

are great mathematical feats Leave us with the factors Three

x minus two why and Acts plus 2 like so

the answer is d