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SAT Math : Algebra

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Example Questions

Example Question #3 : How To Use Foil In The Distributive Property

Expand the following expression:

$(4x+2)(x^2-2)$

Possible Answers:

$x^3+2x^2-8x-4$

$4x^3+2x^2-8x-4$

$4x^3-4$

$4x^3+2x^2+8x+4$

$4x^3+4x-4$

Correct answer:

$4x^3+2x^2-8x-4$

Explanation:

$(4x+2)(x^2-2)=(4x\times x^2)+(4x\times -2)+(2\times x^2) +(2\times -2)$

Which becomes

$4x^3-8x+2x^2-4$

Or, written better

$4x^3+2x^2-8x-4$

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Example Question #4 : How To Use Foil In The Distributive Property

Which of the following is equal to the expression (3x - 1)(2x + 4) ?

Possible Answers:

{5x+3}

6x^2-10

6x^2-4

6x^2+2x+10

6x^2+10x-4

Correct answer:

6x^2+10x-4

Explanation:

Multiply using FOIL:

First = 3x(2x) = 6x²

Outter = 3x(4) = 12x

Inner = -1(2x) = -2x

Last = -1(4) = -4

Combine and simplify:

6x² + 12x - 2x - 4 = 6x² +10x - 4

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Example Question #4 : How To Use Foil In The Distributive Property

Simplify the expression.

(2x^2-3x)(2y+a)

Possible Answers:

2x^2y - 2ax^2 - 3xy - 3ax

-6x^3 + 2ay

-2axy

4x^2y + 2ax^2 - 6xy - 3ax

None of the other answers

Correct answer:

4x^2y + 2ax^2 - 6xy - 3ax

Explanation:

Solve by applying FOIL:

First: 2x² * 2y = 4x²y

Outer: 2x² * a = 2ax²

Inner: –3x * 2y = –6xy

Last: –3x * a = –3ax

Add them together: 4x²y + 2ax² – 6xy – 3ax

There are no common terms, so we are done.

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Example Question #6 : How To Use Foil In The Distributive Property

(6x - 2) (3x + 5) = ax^2 + dx + k

Given the equation above, what is the value of a-d+k ?

Possible Answers:

Correct answer:

Explanation:

(6x - 2) (3x + 5) = ax^2 + dx + k

Use FOIL to expand the left side of the equation.

(6x-2)(3x+5)=18x^2+30x-6x-10=18x^2+24x-10

18x^2+24x-10=ax^2+dx+k

From this equation, we can solve for , , and .

$18x^2=ax^2\rightarrow a=18$

$24x=dx\rightarrow d=24$

-10=k

Plug these values into a-d+k to solve.

a-d+k=(18)-(24)+(-10)=-16

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Example Question #9 : Distributive Property

Expand and simplify the expression.

4(x-5)(2x+10)

Possible Answers:

$8x^{2}-40x+200$

$8x^{2}-200x$

8x^2-10x+10

$8x^{2}-80x-200$

$8x^{2}-200$

Correct answer:

$8x^{2}-200$

Explanation:

4(x-5)(2x+10)

We can solve by FOIL, then distribute the $\small 4$ . Since all terms are being multiplied, you will get the same answer if you distribute the $\small 4$ before using FOIL.

First: x*2x=2x^2

Inside: -5*2x=-10x

Outside: x*10=10x

Last: -5*10=-50

Sum all of the terms and simplify. Do not forget the $\small 4$ in front of the quadratic!

4(2x^2-10x+10x-50)

4(2x^2-50)

Finally, distribute the $\small 4$ .

8x^2-200

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Example Question #2681 : Sat Mathematics

If (5x-4)(5x+4)=16 , what is the value of ?

Possible Answers:

$\pm\frac{4\sqrt{2}}{5}$

$\pm5\sqrt{3}$

$\pm2\sqrt{2}$

$\pm\frac{4}{5}$

$\pm7$

Correct answer:

$\pm\frac{4\sqrt{2}}{5}$

Explanation:

Use the FOIL method to distribute terms and simplify the equation:

(5x-4)(5x+4)=16

$25x^{2}-16=16$

$25x^{2}=32$

$x^{2}=\frac{32}{25}$

$x=\pm \sqrt{\frac{32}{25}}$

$x=\pm \frac{\sqrt{16}\sqrt{2}}{5}$

$x=\pm \frac{4\sqrt{2}}{5}$

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Example Question #2682 : Sat Mathematics

Expand and simplify:

$(2\sqrt{7}+\sqrt{8})^{2}=$

Possible Answers:

$7+8\sqrt{56}$

$36+8\sqrt{14}$

$4+\sqrt{15}$

$8+7\sqrt{15}$

$4\sqrt{15}$

Correct answer:

$36+8\sqrt{14}$

Explanation:

Use the FOIL method in the distributive property to simplify the expression:

$(2\sqrt{7}+\sqrt{8})^{2}$

First simplify the radicals,

$=(2\sqrt{7}+\sqrt{4}\sqrt{2})^{2}$

$=(2\sqrt{7}+2\sqrt{2})^{2}$

$=(2\sqrt{7}+2\sqrt{2})(2\sqrt{7}+2\sqrt{2})$

$=(4)(7)+(4\sqrt{2}\sqrt{7}+4\sqrt{2}\sqrt{7})+(4)(2)$

$=28+4\sqrt{14}+4\sqrt{14}+8$

$=36+8\sqrt{14}$

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Example Question #11 : Distributive Property

Expand the expression $(x^{4}+2x^{3})(4x+9)$ .

Possible Answers:

$6x^{4}+5x^{3}+11x$

$9x^{4}+8x^{3}+11x^{2}$

$4x^{5}+17x^{4}+18x^{3}$

$5x^{4}+13x^{3}+8x^{2}$

$4x^{3}+11x^{2}+13x$

Correct answer:

$4x^{5}+17x^{4}+18x^{3}$

Explanation:

Use the FOIL method (first, outer, inner, last) to multiply expressions and combine like terms:

$(x^{4}+2x^{3})(4x+9)$

$=(x^4 \cdot4x) + (x^4 \cdot 9) + (2x^3 \cdot 4x) + (2x^3\cdot 9)$

$=4x^{5}+9x^{4}+8x^{4}+18x^{3}$

$=4x^{5}+17x^{4}+18x^{3}$

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Example Question #14 : How To Use Foil In The Distributive Property

Simplify: (3x-9)(9-3x)

Possible Answers:

-9x^2+54x-81

-9x^2-81

-9x^2-54x-81

-9x^2+54x+81

-9x^2+54x

Correct answer:

-9x^2+54x-81

Explanation:

Use the FOIL method to simplify. Use the following formula to simplify.

(a+b)(c+d) = ac+ad+bc+bd

Substitute and follow the terms.

(3x-9)(9-3x)

= (3x)(9)+(3x)(-3x)+(-9)(9)+(-9)(-3x)

=27x-9x^2-81+27x

Combine like terms.

The answer is : -9x^2+54x-81

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Example Question #909 : Algebra

Simplify: (3x-5)(x-9)

Possible Answers:

3x^2+22x-45

3x^2-32x-45

3x^2-22x+45

3x^2-22x-45

3x^2-32x+45

Correct answer:

3x^2-32x+45

Explanation:

Use the FOIL method to solve. Follow the example below:

(a+b)(c+d)=ac+ad+bc+bd

(3x-5)(x-9)= (3x)(x)+(3x)(-9)+(-5)(x)+(-5)(-9)

Simplify the expression.

3x^2-27x-5x+45 = 3x^2-32x+45

The answer is: 3x^2-32x+45

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SAT Math : Algebra

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #3 : How To Use Foil In The Distributive Property

Example Question #4 : How To Use Foil In The Distributive Property

Example Question #4 : How To Use Foil In The Distributive Property

Example Question #6 : How To Use Foil In The Distributive Property

Example Question #9 : Distributive Property

Example Question #2681 : Sat Mathematics

Example Question #2682 : Sat Mathematics

Example Question #11 : Distributive Property

Example Question #14 : How To Use Foil In The Distributive Property

Example Question #909 : Algebra

All SAT Math Resources

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