PAGEPAGE11.5平方差公式學(xué)問(wèn)要點(diǎn)基礎(chǔ)練學(xué)問(wèn)點(diǎn)1平方差公式1.(bc+3a)(bc-3a)的結(jié)果是(D)A.b2c2+9a2 B.b2c2-3a2C.-b2c2-9a2 D.-9a2+b2c22.若(2a+3b)()=4a2-9b2,則括號(hào)內(nèi)應(yīng)填的代數(shù)式是(C)A.-2a-3b B.2a+3bC.2a-3b D.3b-2a3.下列各式能用平方差公式計(jì)算的是(B)A.(2a+b)(2b-a) B.-C.(a+b)(a-2b) D.(2x-1)(-2x+1)4.下列各式運(yùn)算結(jié)果為x2-25y2的是(D)A.(-5y+x)(-5y-x)B.(-5y+x)(5y-x)C.(x+5y)(x+5y)D.(-5y-x)(5y-x)學(xué)問(wèn)點(diǎn)2平方差公式的應(yīng)用5.(寧夏中考)已知m+n=12,m-n=2,則m2-n2=24.

6.計(jì)算:(1)1007×993;解:原式=(1000+7)×(1000-7)=10002-72=999951.(2)2024×2024-20252.解:原式=(2024-1)×(2024+1)-20252=20242-1-20252=-1.綜合實(shí)力提升練7.下列各式中,不能用平方差公式計(jì)算的是(A)A.(x-y)(-x+y) B.(-x+y)(-x-y)C.(-x-y)(x-y) D.(x+y)(-x+y)8.若a+b=1,則a2-b2+2b的值為(C)A.4 B.3C.1 D.09.一個(gè)正整數(shù)若能表示為兩個(gè)正整數(shù)的平方差,則稱這個(gè)正整數(shù)為“創(chuàng)新數(shù)”,比如41=212-202,故41是一個(gè)“創(chuàng)新數(shù)”.下列各數(shù)中,不是“創(chuàng)新數(shù)”的是(D)A.16 B.19 C.27 D.3010.計(jì)算x2+14xA.x4+116 B.x4-C.x4-12x2+116 D.x4-18x11.請(qǐng)你計(jì)算:(1-x)(1+x),(1-x)(1+x+x2),…,猜想(1-x)(1+x+x2+…+xn)的結(jié)果是(A)A.1-xn+1 B.1+xn+1C.1-xn D.1+xn12.12x+32-113.計(jì)算:(1)(a+2b)(a-2b)-12b(a-8b解:原式=a2-4b2-12ab+4b2=a2-12(2)(2x-y)(y+2x)-(2y+x)(2y-x).解:原式=4x2-y2-4y2+x2=5x2-5y2.14.化簡(jiǎn)并求值:(1+a)(1-a)+a(a-2),其中a=12解:原式=1-2a.當(dāng)a=12時(shí),原式=0拓展探究突破練15.若a=2,求3(a2+1)(a4+1)(a8+1)(a16+1)的值.解:原式=(22-1)(22+1)(24+1)(28+1)(216+1)=(24-1)·(2