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$\textbf{1)}$
$(3x-5)(7-5x)-(5x+2)(2-3x)$
$=(21x-15x^2-35+25x)-(10x-15x^2+4-6x)$
$=-15x^2+46x-35+15x^2-4x-4$
$=42x-39$
$=3(14x-13).$
a) P(x)=2x^3 - 3x + x^5 - 4x^3 + 4x - x^5 + x^2 - 2
= ( 2x^3 - 4x^3 ) + x^2 + ( -3x + 4x ) + ( x^5 - x^5 ) - 2
= -2x^3 + x^2 + x - 2
Q(x)=x^3 - 2x^2 + 3x +1 - 2x^2
= x^3 + ( -2x^2 - 2x^2 ) + 3x + 1
= x^3 - 4x^2 + 3x + 1
b) M(x) = P(x) - Q(x) = ( -2x^3 + x^2 + x - 2 ) - ( x^3 - 4x^2 + 3x + 1 )
= -2x^3 + x^2 + x - 2 - x^3 + 4x^2 - 3x - 1
= ( -2x^3 - x^3 ) + ( x^2 + 4x^2 ) + ( x - 3x ) + ( - 2 - 1 )
= -3x^3 + 5x^2 - 2x - 3
c) Bậc M(x) là 3
a: \(=\left(x^7+x^7\right)+\left(-3x^4-x^4\right)+\left(2x^3-x^3\right)-x^2-x+5\)
\(=2x^7-4x^4+x^3-x^2-x+5\)
b: \(=-4x^5-3x^4+\left(2x^2-3x^2-x^2\right)-\dfrac{1}{2}x+1\)
\(=-4x^5-3x^4-2x^2-\dfrac{1}{2}x+1\)
a: \(=9x^2-y^2+x^2-2xy+y^2\)
\(=10x^2-2xy+2y^2\)
b: \(=4x^2-9-x^2+6x-9+2x^2+4x-x-2\)
\(=5x^2+9x-16\)
c: \(=\left(2x-1-x-1\right)^2=\left(x-2\right)^2=x^2-4x+4\)
a) 3x(x + 2) + 4x(-2x + 3) + (2x - 3)(3x + 1)
= 3x2 + 6x - 8x2 + 12x + 6x2 + 2x - 9x - 3
= (3x2 - 8x2 + 6x2) + (6x + 12x + 2x - 9x) - 3
= x3 + 11x - 3
b) (x2 + 1)(x2 - x + 2) - (x2 - 1)(x2 + x - 2)
= x4 - x3 + 3x2 - x + 2 - x4 - x3 + 3x2 + x - 2
= (x4 - x4) + (-x3 - x3) + (3x2 + 3x2) + (-x + x) + (2 - 2)
= -2x3 + 6x2
c) (-2x - 3)2 + (3x + 2)2 + (4x + 1)
= 4x2 + 12x + 9 + 9x2 + 12x + 4 + 4x + 1
= (4x2 + 9x2) + (12x + 12x + 4x) + (9 + 4 + 1)
= 13x2 + 28x + 14