Which expression is equivalent to (x + 3)(x - 5)?

Answer: x^2 - 2x - 15 FOIL: x \cdot x + x(-5) + 3 \cdot x + 3(-5) = x^2 - 5x + 3x - 15 = x^2 - 2x - 15.

Which expression is equivalent to (x + 4)^2?

Answer: x^2 + 8x + 16 (x + 4)^2 = x^2 + 2(4)x + 16 = x^2 + 8x + 16.

Answer: (x + 5)^2 Perfect square trinomial: a^2 + 2ab + b^2 = (a+b)^2. Here b = 5, 2ab = 10x. So (x+5)^2.

SAT Math · Topic 2.3

Part of Advanced Math.

Practice questions

107

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Sample 1difficulty 2/5
$(x + 3)(x - 5)$
- A
  $x^2 - 2x - 15$
  check_circle
- B
  $x^2 + 2x - 15$
- C
  $x^2 - 2x + 15$
- D
  $x^2 - 8x - 15$
Why
$x \cdot x + x(-5) + 3 \cdot x + 3(-5) = x^2 - 5x + 3x - 15 = x^2 - 2x - 15$
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Sample 2difficulty 2/5
$(x + 4)^2$
- A
  $x^2 + 16$
- B
  $x^2 + 8x + 16$
  check_circle
- C
  $x^2 + 8x + 8$
- D
  $x^2 + 4x + 16$
Why
$(x + 4)^2 = x^2 + 2(4)x + 16 = x^2 + 8x + 16$
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Sample 3difficulty 2/5
$x^2 + 10x + 25$
- A
  $(x - 5)^2$
- B
  $(x + 25)(x + 1)$
- C
  $(x + 5)^2$
  check_circle
- D
  $(x + 5)(x - 5)$
Why
$a^2 + 2ab + b^2 = (a+b)^2$
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Sample 4difficulty 2/5
$x^2 - 49$
- A
  $(x - 7)^2$
- B
  $(x - 7)(x + 7)$
  check_circle
- C
  $(x + 7)^2$
- D
  $(x - 49)(x + 1)$
Why
$a^2 - b^2 = (a-b)(a+b)$
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Sample 5difficulty 2/5
$\dfrac{x^2 - 9}{x + 3}$
- A
  $x^2 - 3$
- B
  $x + 3$
- C
  $\dfrac{1}{x - 3}$
- D
  $x - 3$
  check_circle
Why
$x^2 - 9 = (x-3)(x+3)$
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