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Class 10 > Learn Mathematics > Evaluate the product without multiplying directly:...
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Evaluate the product without multiplying directly: 103 x 107?

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103 x 107 = (100 + 3)(100 + 7) We know that (x + a)(x + b) = x^2 + (a + b)x + ab Therefore, 103 x 107 = 100^2 + (3 + 7) x 100 + 3 x 7 = 10000 + 1000 + 21 = 11021
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103 +3 107 +7 .................... 11021 103 is 3 above base 100 and 107 is 7 above base 100 103+7=107+3=110 and multiply the deficiencies i.e 3 x 7=21. So, 103 107=11021.
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107x103 = (105+2)x(105-2) = 105^2 - 2^2 = 11025-4 = 11021 Applying formula (a+b)x(a-b) = a^2-b^2. Here, a=105 & b=2
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Their product is 11021. First add 7 to 103 OR add 3 to 107 we get 110 either way. take this 110 as right portion of our answer 110, now multiply 3 and 7, take this product 21 as right portion of the answer. 21 putting the two portions together, we get the product of 103 and 107 as 11021.
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TEACHING IS MY PASSION-I STILL STRIVE TO BETTER MY TEACHING ABILITIES

Their product is 11021. First add 7 to 103 OR add 3 to 107 we get 110 either way. take this 110 as left portion of our answer 110, now multiply 3 and 7, take this product 21 as right portion of the answer. 21 putting the two portions together, we get the product of 103 and 107 as 11021.
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11021.
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