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- NOW WE WANT TO SQUARE BINOMIALS.
IF WE HAVE THE QUANTITY X + 5 SQUARED,
WE NEED TO REMEMBER THAT MEANS WE'RE GOING TO HAVE
2 FACTORS OF X + 5.
SO IT'S THE QUANTITY OF X + 5 x THE QUANTITY X + 5.
AND NOW WE CAN DETERMINE THIS PRODUCT
USING THE FOIL METHOD, OR BY DOUBLE DISTRIBUTION.
THE MOST IMPORTANT THING ABOUT THESE TYPES OF PROBLEMS
IS WE CANNOT MAKE THE ASSUMPTION
THAT IF WE HAVE THE QUANTITY X + 5 SQUARED,
IT'S GOING TO BE EQUAL TO X SQUARED + 5 SQUARED.
THAT IS NOT TRUE.
THIS DOES NOT EQUAL X SQUARED + 25,
AND WE CAN VERIFY THIS BY MULTIPLYING THIS OUT.
SO WE'LL HAVE X x X, X x 5, 5 x X, AND 5 x 5.
SO WE'LL HAVE X x X = X SQUARED.
X x 5 = 5X, SO + 5X.
THEN WE HAVE 5 x X = 5X, AND THEN WE HAVE 5 x 5 = 25.
NOTICE HOW WE MULTIPLY THIS OUT.
WE HAVE TWO LIKE TERMS HERE IN THE MIDDLE.
SO THIS PRODUCT IS X SQUARED + 10X + 25,
WHICH VERIFIES THIS SHORTCUT HERE IS INCORRECT.
LET'S GO AND TAKE A LOOK AT A SECOND EXAMPLE.
AGAIN, BECAUSE THIS IS SQUARED
WE WILL HAVE 2 FACTORS OF 3X + 7,
AND NOW WE'LL MULTIPLY THIS LIKE WE NORMALLY DO.
SO WE'LL HAVE 3X x 3X, 3X x 7, 7 x 3X, AND 7 x 7.
SO 3X x 3X = 9X SQUARED.
3X x 7 = 21X AND THEN 7 x 3X = 21X,
AND THEN 7 x 7 = 49.
AGAIN WE HAVE TWO LIKE TERMS HERE,
SO OUR PRODUCT WOULD BE 9X SQUARED + 42X + 49.
NOW IT IS TRUE THERE IS A FORMULA FOR SQUARING A BINOMIAL.
IF WE HAVE THE QUANTITY "A" + B SQUARED,
IT'S GOING TO BE EQUAL TO "A" SQUARED + 2 x AB + B SQUARED.
IT'S ALSO TRUE IF WE HAVE THE QUANTITY "A" - B SQUARED.
THAT'D BE EQUAL TO "A" SQUARED - 2AB + B SQUARED,
WHERE "A" IS THE FIRST TERM
AND B IS THE SECOND TERM IN THE BINOMIAL.
BUT I'M NOT A BIG FAN OF MEMORIZING THIS,
BECAUSE AS LONG AS YOU KNOW THAT IF SOMETHING IS SQUARED
YOU'LL HAVE TWO EQUAL FACTORS, YOU CAN ALWAYS MULTIPLY IT OUT,
AND DON'T HAVE TO MEMORIZE ANOTHER FORMULA
THAT YOU'LL PROBABLY FORGET IN A WEEK OR TWO.
I HOPE YOU FOUND THIS HELPFUL.