S2-3.3-Ch3 恆等式

Authored by Hoi Wong

Mathematics

8th Grade

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

32.   (4a – 5)(4a + 5) =
       A.   16a² – 25。
       B.    16a² + 25。
       C.   16a² – 40a + 25。
       D.   16a² – 20a + 25。

Answer explanation

32.     (4a – 5)(4a + 5)
            = (4a)² – 5²
            = 16a² – 25
            ∴     答案是A。

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

33.   (–2 – 7p)(–2 + 7p) =
       A.   –4 + 49p²。
       B.    4 – 49p²。
       C.   4 – 14p + 49p²。
       D.   4 + 28p + 49p²。

Answer explanation

33.     (–2 – 7p)(–2 + 7p)
            = (–2)² – (7p)²
            = 4 – 49p²
            ∴     答案是B。

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

34.   5(3x + 10y)(3x – 10y) =
       A.   15x²– 50y²。
       B.    45x² – 500y²。
       C.   15x²– 60xy + 50y²。
       D.   45x²– 60xy – 500y²。

Answer explanation

34.     5(3x + 10y)(3x – 10y)
            = 5[(3x)² – (10y)²]
            = 5(9x² – 100y²)
            = 45x² – 500y²
            ∴     答案是B。

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Answer explanation

35. (x + 5)(x – 5) + r = x² + 25
x² – 5² + r = x² + 25
r – 25 = 25
r = 50
∴ 答案是D。

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

36.   下列何者不是恆等式？Which of the following is NOT an identity?
       A.   (a² – b²)(a² + b²) = a⁴ – b⁴
       B.    (a – b)(a + b)(a² + b²) = (a – b)(a + b)³
       C.   (a – b)(a + b) – (a² + b²) = –2b²
       D.   (a² – b²)(a + b) = (a – b)(a + b)²

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S2-3.3-Ch3 恆等式

32. (4a – 5)(4a + 5) = A. 16a2 – 25。 B. 16a2 + 25。 C. 16a2 – 40a + 25。 D. 16a2 – 20a + 25。

32. (4a – 5)(4a + 5) = (4a)2 – 52 = 16a2 – 25 ∴ 答案是A。

33. (–2 – 7p)(–2 + 7p) = A. –4 + 49p2。 B. 4 – 49p2。 C. 4 – 14p + 49p2。 D. 4 + 28p + 49p2。

33. (–2 – 7p)(–2 + 7p) = (–2)2 – (7p)2 = 4 – 49p2 ∴ 答案是B。

34. 5(3x + 10y)(3x – 10y) = A. 15x2 – 50y2。 B. 45x2 – 500y2。 C. 15x2 – 60xy + 50y2。 D. 45x2 – 60xy – 500y2。

34. 5(3x + 10y)(3x – 10y) = 5[(3x)2 – (10y)2] = 5(9x2 – 100y2) = 45x2 – 500y2 ∴ 答案是B。

35. (x + 5)(x – 5) + r = x2 + 25 x2 – 52 + r = x2 + 25 r – 25 = 25 r = 50 ∴ 答案是D。

36. 下列何者不是恆等式？Which of the following is NOT an identity? A. (a2 – b2)(a2 + b2) = a4 – b4 B. (a – b)(a + b)(a2 + b2) = (a – b)(a + b)3 C. (a – b)(a + b) – (a2 + b2) = –2b2 D. (a2 – b2)(a + b) = (a – b)(a + b)2

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32. (4a – 5)(4a + 5) =
A. 16a² – 25。
B. 16a² + 25。
C. 16a² – 40a + 25。
D. 16a² – 20a + 25。

32. (4a – 5)(4a + 5)
= (4a)² – 5²
= 16a² – 25
∴ 答案是A。

33. (–2 – 7p)(–2 + 7p) =
A. –4 + 49p²。
B. 4 – 49p²。
C. 4 – 14p + 49p²。
D. 4 + 28p + 49p²。

33. (–2 – 7p)(–2 + 7p)
= (–2)² – (7p)²
= 4 – 49p²
∴ 答案是B。

34. 5(3x + 10y)(3x – 10y) =
A. 15x²– 50y²。
B. 45x² – 500y²。
C. 15x²– 60xy + 50y²。
D. 45x²– 60xy – 500y²。

34. 5(3x + 10y)(3x – 10y)
= 5[(3x)² – (10y)²]
= 5(9x² – 100y²)
= 45x² – 500y²
∴ 答案是B。

35. (x + 5)(x – 5) + r = x² + 25
x² – 5² + r = x² + 25
r – 25 = 25
r = 50
∴ 答案是D。

36. 下列何者不是恆等式？Which of the following is NOT an identity?
A. (a² – b²)(a² + b²) = a⁴ – b⁴
B. (a – b)(a + b)(a² + b²) = (a – b)(a + b)³
C. (a – b)(a + b) – (a² + b²) = –2b²
D. (a² – b²)(a + b) = (a – b)(a + b)²