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Algebra II : Simplifying Expressions

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Example Question #53 : How To Use Foil In The Distributive Property

Evaluate the following to its simplest form:

$\frac{1}{2}(4x+2)(x-2)+\frac{1}{3}(2x-3)$

Possible Answers:

$4x^2-2\frac{1}{3}x-3$

$2x^2-2\frac{2}{3}x-3$

None of the available answers

$2x^2-2\frac{1}{3}x-2$

$2x^2-2\frac{1}{3}x-3$

Correct answer:

$2x^2-2\frac{1}{3}x-3$

Explanation:

$\frac{1}{2}(4x+2)(x-2)+\frac{1}{3}(2x-3)$

First we will foil the first function before distributing.

$\frac{1}{2}(4x^2-8x+2x-4)+\frac{1}{3}(2x-3)$

$\frac{1}{2}(4x^2-6x-4)+\frac{1}{3}(2x-3)$

We will then distribute out the $\frac{1}{2}$

$2x^2-3x-2+\frac{1}{3}(2x-3)$

We will then distribute out the $\frac{1}{3}$

$2x^2-3x-2+\frac{2}{3}x-1$

Now the only like terms we have are $-3x+\frac{2}{3}x$ and -2-1 , so our final answer is:

$2x^2-2\frac{1}{3}x-3$

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Example Question #55 : Distributive Property

Simplify the expression: 6(4k+8s)

Possible Answers:

72ks

24k+8s

10k+14s

24k+48s

32ks

Correct answer:

24k+48s

Explanation:

distributes to , multiplying to become 24k , and distributes to , multiplying to make 48s .

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Example Question #31 : Simplifying Expressions

Divide the fractions.

$\frac{30xy}{11} \div \frac{25x^{3}}{22y}$

Possible Answers:

$\frac{5x^{4}}{12}$

$\frac{5x^{2}}{12y^{2}}$

$\frac{5y^{2}}{12x^{2}}$

$\frac{12y^{2}}{5x^{2}}$

$\frac{12x^{4}}{5}$

Correct answer:

$\frac{12y^{2}}{5x^{2}}$

Explanation:

$\frac{30xy}{11} \div \frac{25x^{3}}{22y}$

Dividing fractions is equal to multiplying by the reciprocal.

$\frac{30xy}{11} * \frac{22y}{25x^{3}}$

Cross-cancel the 30 with the 25, and the 22 with the 11.

$\frac{6xy}{1} *\frac{2y}{5x^{3}}$

Combine via multiplication and simplify.

$\frac{6xy* 2y}{5x^{3}}=\frac{6* 2*x* y*y}{5x^{3}}=\frac{12y^{2}}{5x^{2}}$

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Example Question #31 : Simplifying Expressions

Simplify the following expression.

$4x(3x^{2}+x+10)$

Possible Answers:

$12x^{2}+14x$

$7x^{3}+4x^{2}+14x$

$11x^{2}+40x$

None of the other answers

Correct answer:

Explanation:

Distribute the outside term into the parentheses.

$4x(3x^{2}+x+10)=(4x*3x^{2})+(4x *x) +(4x* 10)$

Simplify each distributed factor into one expression.

$12x^{3}+4x^{2}+40x$

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Example Question #32 : Simplifying Expressions

Simplify the following expression.

$5y(3y^{3}-2y+9)$

Possible Answers:

$8y^{4}+3y^{2}+14y$

$15y^{3}+35y$

$8y^{4}-7y^{2}+14y$

None of the other answers.

Correct answer:

Explanation:

Distribute the outside term into the parentheses.

$5y(3y^{3}-2y+9)=(5y* 3y^{3})- (5y* 2y) + (5y*9)$

Simplify each distributed factor into one expression.

$15y^{4}-10y^{2}+45y$

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Example Question #123 : Monomials

Multiply. Give the answer in simplest form.

$\left(\frac{3}{2x^2} \right )\cdot\left(\frac{4x^2y}{9} \right )$

Possible Answers:

$\frac{3y}{2x}$

$\frac{12y}{9}$

$\frac{2y}{3}$

2x^4y

Correct answer:

$\frac{2y}{3}$

Explanation:

Multiplying quotients is similar to multiplying fractions, so we multiply straight across to get $\small \frac{12x^2y}{18x^2}$ . From this point, we can simplify. Since $\small \frac{12}{18}=\frac{2}{3}$ and $\small \frac{x^2}{x^2}=x^{2-2}=x^0=1$ , our final answer becomes $\small \frac{2}{3} \cdot 1 \cdot y = \frac{2y}{3}$ .

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Example Question #5 : How To Subtract Polynomials

Subtract:

$\left (\frac{1}{2}x + \frac{2}{3} \right ) - \left (\frac{1}{4}x - \frac{1}{6} \right )$

Possible Answers:

$-\frac{1}{4}x + \frac{5}{6}$

$\frac{1}{4}x + \frac{5}{6}$

$\frac{1}{4}x + \frac{1}{2}$

$\frac{1}{4}x + \frac{1}{9}$

$-\frac{1}{4}x + \frac{1}{2}$

Correct answer:

$\frac{1}{4}x + \frac{5}{6}$

Explanation:

$\left (\frac{1}{2}x + \frac{2}{3} \right ) - \left (\frac{1}{4}x - \frac{1}{6} \right )$

$=\frac{1}{2}x + \frac{2}{3} - \frac{1}{4}x + \frac{1}{6}$

$=\frac{1}{2}x - \frac{1}{4}x + \frac{2}{3} + \frac{1}{6}$

$=\frac{2}{4}x - \frac{1}{4}x + \frac{4}{6} + \frac{1}{6}$

$=\frac{1}{4}x + \frac{5}{6}$

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Example Question #6 : How To Subtract Polynomials

Subtract:

$(7.5x^{2} + 2.4x - 4.6) - (x^{2} - 3.2x - 1.5)$

Possible Answers:

$7.5x^{2} + 5.6x - 3.1$

$6.5x^{2} -0.8x - 6.1$

$6.5x^{2} + 5.6x - 3.1$

$6.5x^{2} -0.8x - 3.1$

$6.5x^{2} + 5.6x - 6.1$

Correct answer:

$6.5x^{2} + 5.6x - 3.1$

Explanation:

$(7.5x^{2} + 2.4x - 4.6) - (x^{2} - 3.2x - 1.5)$

$= 7.5x^{2} + 2.4x - 4.6 - x^{2} + 3.2x +1.5$

$= 7.5x^{2} - 1x^{2} + 2.4x + 3.2x - 4.6 +1.5$

$= 6.5x^{2} + 5.6x - 3.1$

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Example Question #82 : Expressions

Multiply: $(x -5) (x^{2} +5x + 25)$

Possible Answers:

$x^{3} -20x +125$

$x^{3} -125$

$x^{3} +125$

$x^{3} -20x -125$

$x^{3} -20x^{2} -125$

Correct answer:

$x^{3} -125$

Explanation:

$(x -5) (x^{2} +5x + 16)$

$= x (x^{2} +5x + 25)-5 (x^{2} +5x + 25)$

$= x \cdot x^{2} +x \cdot 5x + x \cdot 25-5 \cdot x^{2} -5 \cdot 5x -5 \cdot 25$

$= x^{3} +5x^{2} +25x-5 x^{2} -25x -125$

$= x^{3} +5x^{2} -5 x^{2} +25x -25x -125$

$= x^{3} -125$

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Example Question #10 : How To Add Trinomials

Add:

(3x^2+14x+9) +(x^2-2x+4)

Possible Answers:

-8x+13

2x^2+16x+5

4x^2+12x+13

4x^4-12x^2+13

3x^4+12x^2+36

Correct answer:

4x^2+12x+13

Explanation:

To add trinomials, identify and group together the like-terms: (3x^2+x^2) +(14x-2x)+(9+4) . Next, factor out what is common between the like-terms: (3+1)x^2+(14-2)x+(9+4) . Finally, add what is left inside the parentheses to obtain the final answer of 4x^2+12x+13 .

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Algebra II : Simplifying Expressions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #53 : How To Use Foil In The Distributive Property

Example Question #55 : Distributive Property

Example Question #31 : Simplifying Expressions

Example Question #31 : Simplifying Expressions

Example Question #32 : Simplifying Expressions

Example Question #123 : Monomials

Example Question #5 : How To Subtract Polynomials

Example Question #6 : How To Subtract Polynomials

Example Question #82 : Expressions

Example Question #10 : How To Add Trinomials

All Algebra II Resources

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