Practice Test \( { }^{4} \) Wilte as a polynomial. \[ \begin{array}{ll} \left(5 x^{2}+3 x-4\right)+\left(3 x^{2}-8 x-2\right)= & \\ \left(4 x^{2}+5 x-8\right)-\left(2 x^{2}-6 x+2\right)= \\ (5 x+7)+(2 x-4)-(3 x+2)= & \\ 3(5 x+2)= & 2 x y(y-x)= \\ a(2-a)= & -4(a-b)= \\ (a+b+5) 3 b= & 3 x\left(x^{2}+x\right)= \end{array} \]
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For the first expression, combine like terms: \[ (5 x^{2}+3 x-4) + (3 x^{2}-8 x-2) = (5 x^{2} + 3 x^{2}) + (3 x - 8 x) + (-4 - 2) = 8 x^{2} - 5 x - 6. \] Now for the second expression, remember to distribute the negative sign: \[ (4 x^{2}+5 x-8) - (2 x^{2}-6 x+2) = (4 x^{2}-2 x^{2}) + (5 x + 6 x) + (-8 - 2) = 2 x^{2} + 11 x - 10. \] Next, in the third expression, the combination of the polynomials is: \[ (5 x + 7) + (2 x - 4) - (3 x + 2) = (5 x + 2 x - 3 x) + (7 - 4 - 2) = 4 x + 1. \] For the fourth expression, distribute the 3: \[ 3(5 x + 2) = 15 x + 6. \] Moving on to \( 2 x y(y-x) \), this is already factored: it expands to \( 2xy^2 - 2x^2y \). For \( a(2-a) \): \[ a(2-a) = 2a - a^2. \] The next expression involves distributing \(-4\): \[ -4(a-b) = -4a + 4b. \] For \( (a+b+5) 3 b \), distribute \( 3b \): \[ 3b(a + b + 5) = 3ab + 3b^2 + 15b. \] Finally, for \( 3x(x^2 + x) \): \[ 3x(x^2+x) = 3x^3 + 3x^2. \] Now, you have your polynomials written out correctly with all terms simplified!
