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Lời giải:
\((3a-2)(2a^2-1)+(a+3)(5-6a^2)\)
\(=3a(2a^2-1)-2(2a^2-1)+a(5-6a^2)+3(5-6a^2)\)
\(=6a^3-3a-4a^2+2+5a-6a^3+15-18a^2\)
\(=(6a^3-6a^3)-(4a^2+18a^2)+(-3a+5a)+2+15\)
\(=-22a^2+2a+17\)
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a.ta có
\(\left(x+3\right)^3+\left(x^2+1\right)\left(x-2\right)=x^3+9x^2+27x+27+x^3-2x^2+x-2\)
\(=2x^3+7x^2+28x+25\)
b.\(\left(2x-1\right)^2-\left(2-x\right)^3=4x^2-4x+1+x^3-6x^2+12x-8\)
\(=x^3-2x^2+8x-7\)
a) (x + 3)3 + (x2 + 1)(x - 2)
= x3 + 9x2 + 27x + 27 + x3 - 2x + x - 2
= x3 + x3 + 9x2 + 27x - 2x + x + 27 - 2
= 2x3 + 9x2 + 26x + 25
b) (2x - 1)2 - (2 - x)3
= 4x2 - 4x + 1 - ( 8 - 12x + 6x2 - x3)
= 4x2 - 4x + 1 - 8 + 12x - 6x2 + x3
= x3 + 4x2 - 6x2 + 12x - 4x + 1 - 8
= x3 - 2x2 + 8x - 7
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Sửa đề: \(5x^2y^2\cdot\left(3x^2\right)^3\)
\(=5x^2y^2\cdot27x^6\)
\(=5\cdot27\cdot x^2\cdot x^6\cdot y^2\)
\(=135x^8y^2\)
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a, \(\left(2x-7\right)^2+\left(2x+7\right)^2-2\left(2x+7\right)\left(2x-7\right)=\left(2x-7-2x-7\right)^2=\left(-14\right)^2=196\)
b, \(\left(5x-3\right)^2-\left(5x+3\right)^2-15\left(2x-1\right)\)
\(=\left(5x-3-5x-3\right)\left(5x-3+5x+3\right)-15\left(2x-1\right)\)
\(=-6.10x-15\left(2x-1\right)\)
\(=-60x-15\left(2x-1\right)=-15\left(4x+2x-1\right)=-15\left(6x-1\right)=-90x+15\)
\(a^3+6a^2+12a+8-a\left(a^2-6a+9\right)\)
\(a^3+6a^2+12a+8-a^3+6a^2-9a\)
\(12a^2+3a+8\)