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\(45^2+33^2-22^2+90.33\)
\(=\left(45^2+90.33+33^2\right)-22^2\)
\(=\left(45+33\right)^2-22^2\)
\(=\left(45+33-22\right).\left(45+33+22\right)\)
\(=56.100=5600\)
\(45^2+33^2-22^2+90.30\)
\(=\left(45^2+90.33+33^2\right)-22^2\)
\(=\left(45^2+2.45.33+33^2\right)-22^2\)
\(=\left(45+33\right)^2-22^2\)
\(=\left(45+33-22\right)\left(45+33+22\right)\)
\(=56.100=5600\)
452 + 332 − 222 + 90.33
= (452 + 90 . 33 + 332) −222
= (45 + 33)2 −222
= (45 + 33 − 22).(45 + 33 + 22)
= 56.100
= 5600
a) \(41\cdot24-41\cdot14+59\cdot24-59\cdot14\)
\(=41\cdot10+59\cdot10\)
\(=1000\)
\(45^2+40^2-10^2+80.45\)
\(=\left(45+40\right)^2-10^2\)
\(=\left(45+40-10\right)\left(45+40+10\right)\)
\(=75.95=7125\)
\(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)
\(=\left(2^{32}-1\right)\)
\(45^2+40^2-15^2+80.45\)
\(=40^2+2.40.45+45^2-15^2\)
\(=\left(40+45\right)^2-15^2\)
\(=\left(40+45-15\right)\left(40+45+15\right)\)
\(=70.100=7000\)