1. Given that y2+my+ 16 is completely flat, the value of m is ().

A8 b . 4 c . 8d . 4

2. The following polynomials can be factorized by the complete square formula ().

a . x2-6x-9 b . a2- 16a+32 c . x2-2xy+4 y2 d . 4a 2-4a+ 1

3. All the following belong to the correct decomposition factor is ()

a . 1+4 x2 =( 1+2x)2 b . 6a-9-a2 =-(a-3)2

c . 1+4m-4 m2 =( 1-2m)2d . x2+xy+y2 =(x+y)2

4. Factorizing x4-2x2y2+y4, the result is ()

A.(x-y)4b .(x2-y2)4c .[(x+y)(x-y)]2d .(x+y)2(x-y)2

Second, fill in the blanks

5. It is known that 9x2-6xy+k is completely flat, so the value of k is _ _ _ _ _.

6.9a2+(________)+25b2=(3a-5b)2

7.-4x2+4xy+(_______)=-(_______)。

8. Given a2+ 14a+49=25, the value of A is _ _ _ _ _ _ _.

Third, answer questions.

9. Break down the following categories:

①a2+ 10a+25②m2- 12mn+36 N2

③xy3-2x2y 2+x3y④(x2+4 y2)2- 16x2y 2

10. Given x=- 19 and y= 12, find the value of the algebraic expression 4x2+ 12xy+9y2.

1 1. It is known that │x-y+ 1│ and x2+8x+ 16 are reciprocal. Find the value of x2+2xy+y2.

Fourth, explore the problem.

12. Do you know all the ideas of mathematics? In solving problems, if we focus on the whole problem, think, associate and explore from all directions, think and deform from the whole, and determine the problem-solving strategies from different aspects, the problem can be solved quickly.

Can you factorize the following equation with holistic thinking method?

①(x+2y)2-2(x+2y)+ 1②(a+b)2-4(a+b- 1)

Reference answer:

1.C 2。 D 3。 B 4。 D 5.y2 6。 -30ab 7。 -y2； 2x-Y 8。 -2 or-12

9.①(a+5)2； ②(m-6n)2； ③xy(x-y)2； ④(x+2y)2(x-2y)2

10.4

1 1.49

12.①(x+2y- 1)2； ②(a+b-2)2