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\(a,\left(x+3\right).\left(x^2-3x+9\right)-\left(54+x^3\right)=x^3+27-54-x^3=-27.\)
\(b,8x^3+y^3-8x^3+y^3=2y^3\)
\(A=x^2-2x+1-x^2+4=5-2x\)
\(B=27x^3+8-x^2+9=27x^3-x^2+17\)
\(C=3x^2y-6xy^2-2x\left(x^2-2x^2y+x^2y^2\right)=3x^2y-6xy^2-2x^3+4x^3y-2x^3y^2\)
Em chỉ cần nhớ hằng đẳng thức và áp dụng là biến đổi được ^^
a)(x + y + z) . (x + y) + (x + y)2
=(y+x)z+2y2+4xy+2x2
=(y+x)(z+2y+2x)
a) (a+b)3- (a-b)3- 2ab
=a3+3a2b+3ab2+b3-(a3-3a2b+3ab2-b3)-2ab
=a3+3a2b+3ab2+b3-a3+3a2b-3ab2+b3-2ab
=2b3+6a2b-2ab
b) (x-2). (x2+2x+4) - x.(x2-1)+x+5
=x3-8-x3+x+x+5
=2x-3
a) \(\left(a^2+b+c\right)^2\)
\(=\left(a^2+b\right)^2+2\left(a^2+b\right)c+c^2\)
\(=a^4+2a^2b+b^2+2a^2c+2bc+c^2\)
b) \(\left(a+b+c\right)^2\)
\(=\left(a+b\right)^2+2\left(a+b\right)c+c^2\)
\(=a^2+2ab+b^2+2ca+2bc+c^2\)
\(\left(a+b+c\right)^3=\left(a+b\right)^3+3\left(a+b\right)c\left(a+b+c\right)+c^3\)
\(=a^3+3ab\left(a+b\right)+b^3+3c\left(a+b\right)\left(a+b+c\right)+c^3\)
\(=a^3+b^3+c^3+3\left(a+b\right)\left(ab+ac+bc+c^2\right)\)
\(=a^3+b^3+c^3+3\left(a+b\right)\left[a\left(b+c\right)+c\left(b+c\right)\right]=a^3+b^3+c^3+3\left(a+b\right)\left(a+c\right)\left(b+c\right)\left(\text{đ}pcm\right)\)
\(VT=a^2c^2+b^2d^2+2abcd+a^2d^2+b^2c^2-2abcd\)
\(VT=a^2c^2+b^2d^2+a^2b^2+c^2d^2\)
\(VT=\left(a^2+b^2\right)\left(c^2+d^2\right)=VP\)
\(a,8x^3+12x^2y+6xy^2+y^3=\left(2x\right)^3+3.\left(2x\right)^2.y+3.2x.y^2+y^3=\left(2x+y\right)^3\)
\(b,x^2-9=x^2-3^2=\left(x-3\right)\left(x+3\right)\)
\(c,4x^2-25=\left(2x\right)^2-5^2=\left(2x-5\right)\left(2x+5\right)\)
a) 3(x - 1)2 - 3x(x - 5) = 3(x2 - 2x + 1) - 3x2 + 15x = 3x2 - 6x + 3 - 3x2 + 15x = 9x + 3 = 21 => x = (21 - 3) : 9 = 18 : 9 = 2
b) 3(x + 2)2 + (2x - 1)2 - 7(x + 3)(x - 3) = 3(x2 + 4x + 4) + 4x2 - 4x + 1 - 7(x2 - 9) = 3x2 + 12x + 12 + 4x2 - 4x + 1 - 7x2 + 63
= 8x + 76 = 36 => x = (36 - 76) : 8 = -40 : 8 = -5
a)\(\left(a+b\right)^2-\left(a-b\right)^2=\left(a^2+2ab+b^2\right)-\left(a^2-2ab+b^2\right)=2ab+2ab=4ab\)
b)\(\left(a+b\right)^3-\left(a-b\right)^3-2b^3=\left(a^3+b^3+3ab\left(a+b\right)\right)-\left(a^3-b^3-3ab\left(a-b\right)\right)-2b^3\)
\(2b^3-2b^3+3ab^2+3ab^2=6ab^2\)