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Factorize:

x^{3}+x-3x^{2}-3

a(a+b)3-3a^{2}b(a+b)

x(x^{3}–y^{3})+3xy-(x–y)

a^{2}x^{2}+(ax^{2}+1)x+a

x^{2}+y-xy-x

x^{3}-2x^{2}y+3xy^{2}-6y^{3}

6ab-b^{2}+12ac-2bc

x(x–2)(x–4)+4x-8

(x+2)(x^{2}+25)-10x^{2}-20x

2a^{2}+2ab+3b^{2}

(a-b+c)^{2}+(b-c+a)^{2}+2(a-b+c)(b-c+a)

a^{2}+b^{2}+2(ab+bc+ca)

4(x-y)^{2}-12(x-y)(x+y)+9(x+y)^{2}

a^{2}-b^{2}+2ab-c^{2}

a^{2}+2ab+b^{2}-c^{2}

a^{2}+4b^{2}-4ab-4c^{2}

xy^{9}–yx^{9}

x^{4}+x^{2}y^{2}+y^{4}

x^{2}-y^{2}-4xz+4z^{2}

x^{2}+6x+10

x^{2}-2x-30

x^{2}-x-6

x^{2}+5x+30

x^{2}+2x-24

2x^{2}-x+

x^{2}+x+

21x^{2}-2x+

5x^{2}+20x+3

2x^{2}+3x+531.9(2a-b)^{2}-4(2a-b)-13

9(2a – b)^{2} –4 (2a – b) – 13

7(x-2y)^{2}-25(x-2y)+12

2(x+y)^{2}-9(x+y)-5

Give possible expressions for the length and breadth of the rectangle having 35y^{2}+13y-12 as its area.

What are the possible expressions for the dimensions of the cuboid whose volume is 3x^{2}-12x.

Factorize each of the following expressions:

p^{3}+27

y^{3}+125

1-27a^{3}

8x^{3}y^{3}+27a^{3}

64a^{3}-b^{3}

-8y^{3}

10x^{4}y-10xy^{4}

54x^{6}y+2x^{3}y^{4}

32a^{2}+108b^{3}

(a-2b)^{3}-512b^{3}

(a+b)^{3}-8(a+b)^{3}

(x+2)^{3}+(x-2)^{3}

8x^{2}y^{3}-x^{5}

1029-3x^{3}

x^{6}+y^{6}

x^{3}y^{3}+1

x^{4}y^{4}-xy

a^{12}+b^{12}

x^{3}+6x^{2}+12x+16

a^{3}+b^{3}+a+b

a^{3}--2a

a^{3}+3a^{2}b^{3}+3ab^{2}+b^{3}-8

8a^{3}-b^{3}-4ax+2bx

Simplify

(i)

(ii)

(iii)

64a^{3}+125b^{3}+240a^{2}b+300ab^{2}

125x^{3}-27y^{3}-225x^{2}y+125xy^{2}

x^{3}+1+x^{2}+2x

8x^{3}+27y^{3}+36x^{2}y+54xy^{2}

a^{3}-3a^{2}b+3ab^{2}-b^{3}+8

x^{3}+8y^{3}+6x^{2}y+12xy^{2}

8x^{3}+y^{3}+12x^{2}y+6xy^{2}

8a^{3}+27b^{3}+36a^{2}b+54ab^{2}

8a^{3}-27b^{3}-36a^{2}b+54ab^{2}

x^{3}-12x(x-4)-64

a^{3}x^{3}-3a^{2}bx^{2}+3ab^{2}x-b^{3}

a^{3}+8b^{3}+64c^{3}-24abc

x^{3}-8y^{3}+27z^{3}+18xyz

27x^{3}-y^{3}-z^{3}-9xyz

x^{3}-y^{3}+125z^{3}+5xyz

8x^{3}+27y^{3}-216z^{3}+108xyz

125+8x^{3}-27y^{3}+90xy

(3x-2y)^{3}+(2y-4z)^{3}+(4z-3x)^{3}

(2x-3y)^{3}+(4z-2x)^{3}+(3y-4z)^{3}

(a-3b)^{3}+(3b-c)^{3}+(c-a)^{3}

2a^{3}+3b^{3}+c^{3}-3abc

3a^{3}-b^{3}-5c^{3}-3abc

8x^{3}-125y^{3}+180xy+216

2a^{3}+16b^{3}+c^{3}-12abc

Find the value of x^{3}+y^{3}-12xy+64,whenx+y=-4.

Multiply:

(i) x^{2}+y^{2}+z^{2}-xy+xz+yzbyx+y-z

(ii) x^{2}+4y^{2}+z^{2}+2xy+xz-2yzbyx-2y-z

(iii) x^{2}+4y^{2}+2xy+-3x+6y+9byx-2y+3

(iv) 9x^{2}+25y^{2}+15xy+12x-20y+16by3x-5y+4

Factorize: x^{4}+x^{2}+25.

Factorize: x^{2}-1-2a–a^{2}.

If a + b + c = 0, then write the value of a^{3}+b^{3}+c^{3}.

Ifa^{2}+b^{2}+c^{2}=20,anda+b+c=0,findab+bc+ca.

If a + b + c = 9 and ab + bc + ca = 40, find a^{2} + b^{2} + c^{2}.

If a^{2} + b^{2} + c^{2} = 250 and ab + bc + ca = 3, find a + b + c.

Write the value of: 25^{3}–75^{3}+50^{3}.

Write the value of: 48^{3}–30^{3}-18^{3}.

Write the value of:

Write the value of: 30^{3}+20^{3}-50^{3}.

The factors of a^{2}-1-2x-x^{2} are

The factors of x^{4}+x^{2}=25 are

The factors of x^{2}+4y^{2}+4y-4xy-2x-8 are

The factors of x^{3}-x^{2}y-xy^{2}+y^{3}are

The factors of x^{3}-1+y^{3}+3xyare

The factors of 8a^{2}+b^{3}-6ab+1are

(x+y)^{3}-(x-y)^{3} can be factorized as:

The factors of x^{2}-7x+6are

The expression (a-b)^{3}+(b-c)^{3}+(c-a)^{3} can be factorized as:

The expression x^{4}+4 can be factorized as

If 3x=a+b+c, then the value of (x-a)^{3}+(x-b)^{3}+(x-c)^{3}-3(x-a)(x-b)(x-c) is

If (x+y)^{3}-(x-y)^{3}-6y(x^{2}-y^{2})=ky^{2} then k=

Ifx^{3}-3x^{2}+3x-7=(x+1)(ax^{2}+bx+c), then a+b+c=

The value ofis

The value of is