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SAT Math : SAT Mathematics

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Example Questions

Example Question #9 : Distributive Property

Expand and simplify the expression.

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

Possible Answers:

$8x^{2}-200$

8x^2-10x+10

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

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

$8x^{2}-200x$

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 #901 : Algebra

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

Possible Answers:

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

$\pm7$

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

$\pm5\sqrt{3}$

$\pm2\sqrt{2}$

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 #2681 : Sat Mathematics

Expand and simplify:

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

Possible Answers:

$4+\sqrt{15}$

$7+8\sqrt{56}$

$4\sqrt{15}$

$36+8\sqrt{14}$

$8+7\sqrt{15}$

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 #2682 : Sat Mathematics

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

Possible Answers:

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

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

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

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

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

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

A = 4x+ 7y

B = 5x- 2y

Which of the following expressions is equivalent to ?

Possible Answers:

$20x^{2} - 14y^{2}$

$20x^{2}-27xy- 14y^{2}$

$20x^{2}+ 27xy- 14y^{2}$

9x-5y

$9x^{2} - 9y^{2}$

Correct answer:

$20x^{2}+ 27xy- 14y^{2}$

Explanation:

Using the FOIL method for multiplying binomial expressions:

= (4x +7y)(5x-2y)

$= 4x \cdot 5x - 4x \cdot 2y + 7y \cdot 5x - 7y \cdot 2y$

$= 4 \cdot 5\cdot x \cdot x - 4 \cdot 2\cdot x \cdot y + 7 \cdot 5 \cdot y\cdot x - 7 \cdot 2 \cdot y \cdot y$

$= 20 x^{2} - 8xy + 35xy - 14 y^{2}$

$= 20 x^{2} + 27xy - 14 y^{2}$

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Example Question #15 : How To Use Foil In The Distributive Property

Use FOIL to multiply the expressions:

(5x+6)(x-3)

Possible Answers:

$5x^{2}-9x-18$

$5x^{2}-12x-18$

$x^{2}-9x-18$

$3x^{2}-15x-9$

Correct answer:

$5x^{2}-9x-18$

Explanation:

The term FOIL stands for First, Outside, Inside, Last. It refers to the order in which you distribute between the two expressions, which allows each monomial to multiplied by each monomial in the neighboring expression. For this problem that would look like this:

(5x+6)(x-3)

(5x*x)+(5x*(-3))+(6*x)+(6*(-3))

$5x^{2}-15x+6x-18$

$5x^{2}-9x-18$

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Example Question #16 : How To Use Foil In The Distributive Property

Use FOIL to multiply the expressions:

$(2x-4)(x^{2}+5)$

Possible Answers:

$2x^{3}-4x^{2}-10x-15$

$2x^{3}-4x^{2}+10x-20$

$x^{3}+4x^{2}+10x-20$

$2x^{3}+2x^{2}-10x-20$

Correct answer:

$2x^{3}-4x^{2}+10x-20$

Explanation:

$(2x-4)(x^{2}+5)$

$(2x*x^{2})+(2x*5)+(x^{2}*(-4))+(5*(-4))$

$2x^{3}+10x-4x^{2}-20$

$2x^{3}-4x^{2}+10x-20$

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Example Question #18 : How To Use Foil In The Distributive Property

Use FOIL to multiply the expressions:

(x+10)(5x-6)

Possible Answers:

$5x^{2}-44x+60$

$x^{2}+44x-60$

$5x^{2}+32x-25$

$5x^{2}+44x-60$

Correct answer:

$5x^{2}+44x-60$

Explanation:

(x+10)(5x-6)

(x*5x)+(x*(-6))+(10*5x)+(10*(-6))

$5x^{2}-6x+50x-60$

$5x^{2}+44x-60$

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #9 : Distributive Property

Example Question #901 : Algebra

Example Question #2681 : Sat Mathematics

Example Question #2682 : Sat Mathematics

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

Example Question #909 : Algebra

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

Example Question #15 : How To Use Foil In The Distributive Property

Example Question #16 : How To Use Foil In The Distributive Property

Example Question #18 : How To Use Foil In The Distributive Property

All SAT Math Resources

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