Արձակուրդային տնային աշխատանք հանրահաշվից

առ.6
1) (x+2)(x-3)=x^2-3x+2x-6=x^2-x-6

2) (5x+1)(2x+4)=10x^2+20x+2x+4=10x^2+22x+4

3) (3b+2)(4-b)=12b-3b^2+8-2b=10b-3b^2+8=-3b^2+10b+8

4) (4a^2+5b^2)(3a^2-4b^2)=12a^4-16a^2b^2+15a^2b^2-20b^4=12a^4-a^2b^2-20b^4

5) (4x^2-xy+2y^2)(3x-2y) =12x^3-20x^2y-3x^2y+5xy^2+6xy^2-10y^3=12x^3-23x^2y+11xy^2-10y^3=

առ.7

1) (a^3)^2=a^6

2) (-x^5)^4=x^20

3) (-6c^4)^2=6c^8

4) (2x^2y^3)^5=2x^10y^15

5) (-b^4n)^3=b^12n

առ.8

1) 5b:b=5

2)6mn:3n=2mn^2

3)8ab:4b=2ab^2

4)a^m-a^n=a^m-n

5)20z:5z=4z^2

Առ.9

1) (m+n)^2=m^2+2mn+n^2

2) (x+5)^2=x^2+10x+25

3) (x+1)^2=x^2+2x+2

4) (c-d)^2=c^2-2cd+d^2

5) (x^2+y^2)=x^4+2x^2y^2+y^4

Առ.14

1) (a-b)^3=a^3-3a^2b+3ab^2-b^3

2) (x+y)^3=x^3+3x^2y+3xy^2+y^3

3) (3-m)^3=-m^3+9m^2-27m+27

4) (p+q)^3=p^3+3p^2q+3pq^2+q^3

5) (a+4b)^3=a^3+12a^3b+48ab^2+64b^3

Առ.19

1) ax+bx+cx=x×(a+b+c)

2) 3ab+9ac+12ad=3a×(b+3c+4d)

3) 4ax-8ax^2+12ax^3=4ax×(1-2x+3x^2)

4) 6a^3x-a^2x-a^3b^3=a^2×(6ax-x-ab^)

5) 5x-15xy+10ax=5x(1-3y+2a)
Առ.21

1) 2a(b+c)+b+c=2ab+2ac+b+c

2) 3a(x+y)-x-y=3ax+3ay-x-y

3) 2y(x-y)-x-y=2xy-2y^2-x-y

4) a(x-y)+bx-by=ax-ay+bx-by

5) 3b(a+b)-a-b=3ba+3b^2

Առ.22

1) 25-x^2=(5-x)(5+x)

2) c^2-36=(c-6)(c+6)

3) 4x^2-9=(2x-3)(2x+3)

4) a^2b^2-4=(ab-2)(ab+2)

5) 36p^2-25=(6p-5)(6p+5)

Առ.23

1) (1+x)^2-(y-z)^2=1+2x+x^2-y^2+2yz-z^2

2) (m^2-n)^2-(1+p^2)^2=m^4-2m^2n+n^2-1-2p^2-p^4

3) (2x+3)^2-(x-1)^2=4x^2+12x-x^2+2x-1

4) (3a-2b)^2-(a+b)^2=6a^2-12ab+4b^2-a^2-2ab-b^2

5) (x+2y)^2-(x-1)=x^2+4xy+4y^2-x^2+2x-1

Առ.24

1) a^2+2ab+b^2=(a+b)^2
2) a^2-6a+9=(a-3)^2

3) 4a^2+4a+1=(2a+1)^2

4) x^4-2x^2y+y^2=(x^2-y)

5) 4a^4-4a^2b^2+b^4=(2a^2-b^2)^2

Առ.25

1) a^3+3 a^2b+3ab^2+b^3=(a+b)^3

2) x^3- 3x^2y+3xy^2-y^3=(x-y)^3

3) m^3+6m^2n+12mn^2+8n^3=(m+2n)^3

4) 64+48a^2-96a-8a^3=-8(a-2)^3

5)a^3-6a^2b+12ab-8b^3=(a-2b)^3

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