Toán Lớp 8: Rút gọn biểu thức:
a/(x+2)(x²-2x+4)(x³+2)
b/(x²+1)(x-3)-(x-3)(x²+3x+9)
c/2(x+y)²-3(x-y)²-(x-y)(x+y)
d/(x+1)³-x²(x+3)
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Toán Lớp 8: Rút gọn biểu thức:
a/(x+2)(x²-2x+4)(x³+2)
b/(x²+1)(x-3)-(x-3)(x²+3x+9)
c/2(x+y)²-3(x-y)²-(x-y)(x+y)
d/(x+1)³-x²(x+3)
Comments ( 1 )
Giải đáp:
a) $(x+2)(x^2-2x+4)(x^3+2)=x^6+10x^3+16$
b) $(x^2+1)(x-3)-(x-3)(x^2+3x+9)=-3x^2+x+24$
c) $2(x+y)^2-3(x-y)^2-(x-y)(x+y)=-2x^2+10xy$
d) $(x+1)^3-x^2(x+3)=3x+1$
Lời giải và giải thích chi tiết:
a)
$(x+2)(x^2-2x+4)(x^3+2)\\=(x+2)(x^2-2.x+2^2)(x^3+2)\\=(x^3+2^3)(x^3+2)\\=(x^3+8)(x^3+2)\\=x^3.x^3+2x^3+8x^3+16\\=x^6+10x^3+16$
b)
$(x^2+1)(x-3)-(x-3)(x^2+3x+9)\\=(x-3)(x^2+1-x^2-3x-9)\\=(x-3)(-3x-8)\\=x.(-3x)+x.(-8)-3.(-3x)-3.(-8)\\=-3x^2-8x+9x+24\\=-3x^2+x+24$
c)
$2(x+y)^2-3(x-y)^2-(x-y)(x+y)\\=2(x^2+2xy+y^2)-3(x^2-2xy+y^2)-(x^2-y^2)\\=2x^2+4xy+2y^2-3x^2+6xy-3y^2-x^2+y^2\\=-2x^2+10xy$
d)
$(x+1)^3-x^2(x+3)\\=x^3+3.x^2.1+3.x.1^2+1^3-x^2.x-x^2.3\\=x^3+3x^2+3x+1-x^3-3x^2\\=3x+1$