Question

A)Subtract the following polynomials 1) (75 x²+ 23+13) - (15 x² - X+40)2) (f+9)-(12f+9)3) (2x+43) - (-3X-9)B) Simplify and solve the following polynomials 1) (23d^3 + (7g^9)^132) 34x(2x-11)3) 2m(m+3n)

Answer 1

(A) Subtract the following polynomials;

$(2x+43)-(-3x-9)$

Note that the negative sign affects all terms in the right side parenthesis;

$\begin{gathered} 2x+43-(-3x)-(-9) \\ =2x+43+3x+9 \\ =2x+3x+43+9 \\ =5x+52 \end{gathered}$$\begin{gathered} (f+9)-(12f+9) \\ =f+9-(+12f)-(+9) \\ =f+9-12f-9 \\ =f-12f+9-9 \\ =-11f \end{gathered}$$\begin{gathered} (75x^2+23x+13)-(15x^2-x+40) \\ =75x^2+23x+13-(+15x^2)-(-x)-(+40) \\ =75x^2+23x+13-15x^2+x-40 \\ =75x^2-15x^2+23x+x+13-40 \\ =60x^2+24x-27 \end{gathered}$

(B) Simplify and solve the following polynomials;

$23d^3+(7g^9)^{13}$

Here we'll apply the rule of exponents which is;

$(x^a)^b=x^{a\cdot b}=x^{ab}$

We now have;

$\begin{gathered} 23d^3+(7g^9)^{13} \\ =23d^3+7g^{9\cdot13} \\ =23d^3+7g^{117} \end{gathered}$$\begin{gathered} 34\times(2x-11) \\ =(\lbrack34\cdot2x\rbrack-\lbrack34\cdot11\rbrack)_{} \\ =68x-374 \end{gathered}$$\begin{gathered} 2m(m+3n) \\ =\lbrack2m\cdot m\rbrack+\lbrack2m\cdot3n\rbrack \\ =2m^2+6mn \end{gathered}$