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電子課本網(wǎng) 第27頁

第27頁

信息發(fā)布者:
?$=4(a^2+4a+4)-7(a^2-9)+3(a^2-2a+1)$?
?$=4a^2+16a+16-7a^2+63+3a^2-6a+3$?
?$=10a+82$?
?$=(2a-3)^2-b^2$?
?$=4a^2-12a+9-b^2$?
?$(a + b)^{2}=a^{2}+2ab + b^{2}$?
解:?$(2)$?∵?$(a + b)^2 = a^2 + 2ab + b^2$?
已知?$a + b = 10,$??$ab = 16$?
∴?$a^2 + b^2=(a + b)^2 - 2ab = 10^2 - 2×16 = 100 - 32 = 68$?
?$ (3)$?設(shè)?$8 - x = m,$??$x - 2 = n$?
則?$m + n = 8 - x + x - 2 = 6,$??$\mathrm {m^2} + n^2 = 22$?
∵?$(m + n)^2 =\mathrm {m^2} + 2\ \mathrm {m}n + n^2$?
∴?$mn=\frac {(m + n)^2 - (\mathrm {m^2} + n^2)}2=\frac {6^2 - 22}2=\frac {36 - 22}2=7$?
?$ $?即這個(gè)長方形面積為?$7$?
解:?$(1) S_{1}=a^2-b^2,$??$S_{2}=(a + b)(a - b)$?
?$ (2) $?由?$S_{1}=S_{2}$?可得乘法公式?$(a + b)(a - b)=a^2-b^2$?
?$ (3)(2 + 1)(2^2 + 1)(2^4 + 1)(2^8 + 1) + 1$?
?$ =(2 - 1)(2 + 1)(2^2 + 1)(2^4 + 1)(2^8 + 1) + 1$?
?$ =(2^2 - 1)(2^2 + 1)(2^4 + 1)(2^8 + 1) + 1$?
?$ =(2^4 - 1)(2^4 + 1)(2^8 + 1) + 1$?
?$ =(2^8 - 1)(2^8 + 1) + 1$?
?$ =2^{16} - 1 + 1$?
?$ =2^{16}$?