a) \(105^3-15.105^2+75.105-125\)
\(=105^3-3.105^2.5+3.105.5^2-5^3\)
\(=\left(105-5\right)^3\)
\(=100^3=1000000\)
b) \(63^2-27^2+72^2-18^2\)
\(=\left(63-27\right)\left(63+27\right)+\left(72-18\right)\left(72+18\right)\)
\(=36.90+54.90\)
\(=90.90=8100\)
A= 1000000
B=8100
a)
= \(105^3-3\cdot105^2\cdot5+3\cdot105\cdot5^2-5^3\)
= \(\left(105-5\right)^3\)
\(=100^3=1000000\)
b)
= \(\left(63-27\right)\left(63+27\right)+\left(72-18\right)\left(72+18\right)\)
= \(36\cdot90+54\cdot90\)
= \(90\left(36+54\right)\)
\(=90\cdot90\)
\(=90^2=8100\)
1053 - 15.1052 + 75.105 - 125
= 1053 - 3.5.1052 + 3.52.105 - 53
= ( 105 - 5 )3
= 1003 = 1 000 000
632 - 272 + 722 - 182
= ( 632 - 272 ) + ( 722 - 182 )
= ( 63 - 27 )( 63 + 27 ) + ( 72 - 18 )( 72 + 18 )
= 36.90 + 54.90
= 90( 54 + 36 )
= 90 . 90 = 8100
