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the product of A and B is equal to 2 and
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the sum of A and B is equal to
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7 find the sum of the fourth powers of A
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B as usual pause the video and try to
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solve the problem yourself we begin with
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the standard formula for the square of a
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sum A + B which is equal to the square
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of the first term plus the square of the
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second term plus twice the product of A
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and B we subtract twice the product of A
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and B from the square of the sum and we
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express the sum of the squares a 2 + b 2
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we get the sum of a 2 and b^2 = a + b^ 2
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- 2 * a b now let's write the same
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formula but for the square of the sum of
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the squares of A and B that is instead
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of a we take a squ and instead of B we
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take B squared by the same formula it
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will be equal to the square of the first
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term plus the square of the second term
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Plus twice the product of the squares
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when raising a power to a power the
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exponents multiply so a squar or squared
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becomes a to the 4th and b^ 2 all SAR
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becomes B to the 4th we subtract twice
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the product of the squares of A and B
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from the square of the sum of the
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squares and we express the sum of the
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fourth powers of A and B we get the sum
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of a to the 4th and B to the 4th equal
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the square of a 2 + b^ 2 - 2 * a 2 b^ 2
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we replace the sum of the squares of A
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and B with the difference we get a + b -
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2 and all of this squared minus 2 * the
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product of the squares of A and B
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alternatively this can be written as 2 a
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b and all of this squared by condition
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the sum of a and b equals 7 and the
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product of a and b equals 2 substituting
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these values we get 7^ 2 - 2 * 2 and all
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of this SAR - 2^2 which = 45 - 8 to find
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the square of such a number for example
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for 252 we multiply two by the next
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number three and add 25 which gives us
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625 similarly for 75 squ we multiply 7
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by the next number 8 giving 56 and we
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add 25 in the same way we can find the
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square of a three-digit number for
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example 9995 we take 99 multiply it by
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the next number 100 get 99,900 and add
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9,925 so to find 45 squared we multiply
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four by the next number five getting 20
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and we add 25 giving 2025 - 8 which
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equal 27 the answer is the sum of the
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fourth powers of a and b equals
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2017 the problem is solved if you
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understood the solution like the video
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leave a comment and don't forget to
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