Chapter 4

Simplify the algebraic expressions for the following problems. $$ x(x-7)(x+4) $$

For the following problems, perform the multiplications and combine any like terms. $$ (x+1)^{2} $$

Simplify the algebraic expressions for the following problems. $$ m^{2} n(m+n)(m+2 n) $$

For the following problems, perform the multiplications and combine any like terms. $$ (x-5)^{2} $$

Simplify the algebraic expressions for the following problems. $$ (b+2)\left(b^{2}-2 b+3\right) $$

For the following problems, perform the multiplications and combine any like terms. $$ (a+2)^{2} $$

Simplify the algebraic expressions for the following problems. $$ 3 p\left(p^{2}+5 p+4\right)\left(p^{2}+2 p+7\right) $$

For the following problems, perform the multiplications and combine any like terms. $$ (a-9)^{2} $$

Simplify the algebraic expressions for the following problems. $$ (a+6)^{2} $$

For the following problems, perform the multiplications and combine any like terms. $$ -(3 x-5)^{2} $$

Simplify the algebraic expressions for the following problems. $$ (x-2)^{2} $$

Simplify the algebraic expressions for the following problems. $$ (2 x-3)^{2} $$

For the following problems, perform the multiplications and combine any like terms. $$ -(8 t+7)^{2} $$

Simplify the algebraic expressions for the following problems. $$ \left(x^{2}+y\right)^{2} $$

For the following problems, perform the indicated operations and combine like terms. $$ 3 x^{2}+5 x-2+\left(4 x^{2}-10 x-5\right) $$

Simplify the algebraic expressions for the following problems. $$ (2 m-5 n)^{2} $$

For the following problems, perform the indicated operations and combine like terms. $$ -2 x^{3}+4 x^{2}+5 x-8+\left(x^{3}-3 x^{2}-11 x+1\right) $$

Simplify the algebraic expressions for the following problems. $$ \left(3 x^{2} y^{3}-4 x^{4} y\right)^{2} $$

For the following problems, perform the indicated operations and combine like terms. $$ -5 x-12 x y+4 y^{2}+\left(-7 x+7 x y-2 y^{2}\right) $$

Simplify the algebraic expressions for the following problems. $$ (a-2)^{4} $$

For the following problems, perform the indicated operations and combine like terms. $$ \left(6 a^{2}-3 a+7\right)-4 a^{2}+2 a-8 $$

Find the domain of the equations for the following problems. $$ y=8 x+7 $$

For the following problems, perform the indicated operations and combine like terms. $$ \left(5 x^{2}-24 x-15\right)+x^{2}-9 x+14 $$

Find the domain of the equations for the following problems. $$ y=5 x^{2}-2 x+6 $$

For the following problems, perform the indicated operations and combine like terms. $$ \left(3 x^{3}-7 x^{2}+2\right)+\left(x^{3}+6\right) $$

Find the domain of the equations for the following problems. $$ y=\frac{4}{x-2} $$

For the following problems, perform the indicated operations and combine like terms. $$ \left(9 a^{2} b-3 a b+12 a b^{2}\right)+a b^{2}+2 a b $$

For the following problems, perform the indicated operations and combine like terms. $$ 6 x^{2}-12 x+\left(4 x^{2}-3 x-1\right)+4 x^{2}-10 x-4 $$

Find the domain of the equations for the following problems. $$ z=\frac{4 x+5}{y+10} $$

For the following problems, perform the indicated operations and combine like terms. $$ 5 a^{3}-2 a-26+\left(4 a^{3}-11 a^{2}+2 a\right)-7 a+8 a^{3}+20 $$

For the following problems, perform the indicated operations and combine like terms. $$ 2 x y-15-(5 x y+4) $$

For the following problems, perform the indicated operations and combine like terms. Add \(4 x+6\) to \(8 x-15\)

For the following problems, perform the indicated operations and combine like terms. Add \(5 y^{2}-5 y+1\) to \(-9 y^{2}+4 y-2\)

Add \(3(x+6)\) to \(4(x-7)\)

Add \(-2\left(x^{2}-4\right)\) to \(5\left(x^{2}+3 x-1\right)\).

Add four times \(5 x+2\) to three times \(2 x-1\).

Add five times \(-3 x+2\) to seven times \(4 x+3\).

Add -4 times \(9 x+6\) to -2 times \(-8 x-3\).

Substract \(a^{2}-16\) from \(a^{2}-16\).

Simplify \(\left(\frac{15 x^{2} y^{6}}{5 x y^{2}}\right)^{4}\)

Express the number 198,000 using scientific notation.

How many \(4 a^{2} x^{3}\) 's are there in \(-16 a^{4} x^{5}\) ?

State the degree of the polynomial \(4 x y^{3}+3 x^{5} y-5 x^{3} y^{3},\) and write the numerical coefficient of each term.

Simplify \(3(4 x-5)+2(5 x-2)-(x-3)\).