S2-3.2-Ch3 恆等式

Quiz

•

Mathematics

•

8th Grade

•

Practice Problem

•

Hard

Hoi Wong

Used 6+ times

FREE Resource

7 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

37.   (3x + 10)² =
       A.   9x² + 100。
       B.    3x² + 30x + 100。
       C.   9x² + 30x + 100。
      D.   9x² + 60x + 100。

A

B

C

D

Answer explanation

37. (3x + 10)²
= (3x)² + 2(3x)(10) + 10²
= 9x² + 60x + 100
∴ 答案是D。

2.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

38. (7 – 9m)² =
       A.    81m² – 126m + 49。
       B.    81m² – 63m + 49。
       C.    49 + 63m – 81m²。
       D.    49 + 126m – 81m²。

A

B

C

D

Answer explanation

38. (7 – 9m)²
= 7² – 2(7)(9m) + (9m)²
= 49 – 126m + 81m²
= 81m² – 126m + 49
∴ 答案是A。

3.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

A

B

C

D

Answer explanation

4.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

A

B

C

D

Answer explanation

5.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

41. –3(–p + q)² =
       A.    9p² + 9q²。
       B.    3p² – 6pq + 3q²。
       C.    –3p² + 6pq – 3q²。
       D.    –9p² + 18pq + 9q²。

A

B

C

D

Answer explanation

41.
–3(–p + q)²
=–3[(–p)² + 2(–p)(q) + q²]
= –3(p² – 2pq + q²)
= –3p² + 6pq – 3q²
∴ 答案是C。

6.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

42. [–(a – 5b)]² =
       A.   a² – 25b²。
       B.    a² – 10ab + 25b²。
       C.   –a² + 10ab + 25b²。
       D.    –a² + 10ab – 25b²。

A

B

C

D

Answer explanation

42. [–(a – 5b)]²
= [–(a – 5b)] ´ [–(a – 5b)]
= (a – 5b)²
= a² – 2(a)(5b) + (5b)²
= a² – 10ab + 25b²
∴ 答案是B。

7.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

43. (x – y)² – (x + y)² =
       A.   –4xy。
       B.    4xy。
       C.   x² – y²。
       D.   2x² – 4xy + 2y²。

A

B

C

D

Answer explanation

43. (x – y)² – (x + y)²
=x²–2(x)(y)+y²–
[x²+2(x)(y)+y²]
=x²–2xy + y²–(x² + 2xy +y²)
= x² – 2xy + y² – x² – 2xy – y²
= x² – x² – 2xy – 2xy + y² – y²
= –4xy
∴ 答案是A。

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S2-3.2-Ch3 恆等式

7 questions

37. (3x + 10)2 = A. 9x2 + 100。 B. 3x2 + 30x + 100。 C. 9x2 + 30x + 100。 D. 9x2 + 60x + 100。

37. (3x + 10)2 = (3x)2 + 2(3x)(10) + 102 = 9x2 + 60x + 100 ∴ 答案是D。

38. (7 – 9m)2 = A. 81m2 – 126m + 49。 B. 81m2 – 63m + 49。 C. 49 + 63m – 81m2。 D. 49 + 126m – 81m2。

38. (7 – 9m)2 = 72 – 2(7)(9m) + (9m)2 = 49 – 126m + 81m2 = 81m2 – 126m + 49 ∴ 答案是A。

41. –3(–p + q)2 = A. 9p2 + 9q2。 B. 3p2 – 6pq + 3q2。 C. –3p2 + 6pq – 3q2。 D. –9p2 + 18pq + 9q2。

41. –3(–p + q)2=–3[(–p)2 + 2(–p)(q) + q2]= –3(p2 – 2pq + q2)= –3p2 + 6pq – 3q2 ∴ 答案是C。

42. [–(a – 5b)]2 = A. a2 – 25b2。 B. a2 – 10ab + 25b2。 C. –a2 + 10ab + 25b2。 D. –a2 + 10ab – 25b2。

42. [–(a – 5b)]2 = [–(a – 5b)] ´ [–(a – 5b)]= (a – 5b)2 = a2 – 2(a)(5b) + (5b)2 = a2 – 10ab + 25b2∴ 答案是B。

43. (x – y)2 – (x + y)2 = A. –4xy。 B. 4xy。 C. x2 – y2。 D. 2x2 – 4xy + 2y2。

43. (x – y)2 – (x + y)2 =x2–2(x)(y)+y2–[x2+2(x)(y)+y2]=x2–2xy + y2–(x2 + 2xy +y2)= x2 – 2xy + y2 – x2 – 2xy – y2= x2 – x2 – 2xy – 2xy + y2 – y2= –4xy ∴ 答案是A。

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37. (3x + 10)² =
A. 9x² + 100。
B. 3x² + 30x + 100。
C. 9x² + 30x + 100。
D. 9x² + 60x + 100。

37. (3x + 10)²
= (3x)² + 2(3x)(10) + 10²
= 9x² + 60x + 100
∴ 答案是D。

38. (7 – 9m)² =
A. 81m² – 126m + 49。
B. 81m² – 63m + 49。
C. 49 + 63m – 81m²。
D. 49 + 126m – 81m²。

38. (7 – 9m)²
= 7² – 2(7)(9m) + (9m)²
= 49 – 126m + 81m²
= 81m² – 126m + 49
∴ 答案是A。

41. –3(–p + q)² =
A. 9p² + 9q²。
B. 3p² – 6pq + 3q²。
C. –3p² + 6pq – 3q²。
D. –9p² + 18pq + 9q²。

41.
–3(–p + q)²
=–3[(–p)² + 2(–p)(q) + q²]
= –3(p² – 2pq + q²)
= –3p² + 6pq – 3q²
∴ 答案是C。

42. [–(a – 5b)]² =
A. a² – 25b²。
B. a² – 10ab + 25b²。
C. –a² + 10ab + 25b²。
D. –a² + 10ab – 25b²。

42. [–(a – 5b)]²
= [–(a – 5b)] ´ [–(a – 5b)]
= (a – 5b)²
= a² – 2(a)(5b) + (5b)²
= a² – 10ab + 25b²
∴ 答案是B。

43. (x – y)² – (x + y)² =
A. –4xy。
B. 4xy。
C. x² – y²。
D. 2x² – 4xy + 2y²。

43. (x – y)² – (x + y)²
=x²–2(x)(y)+y²–
[x²+2(x)(y)+y²]
=x²–2xy + y²–(x² + 2xy +y²)
= x² – 2xy + y² – x² – 2xy – y²
= x² – x² – 2xy – 2xy + y² – y²
= –4xy
∴ 答案是A。