could someone help me with this assignment in Algebra?

Question

1) (x + 2y + 2z)sqare
2) (2x + 3y - 4z + 3w)square
3) (xsquare - 2x + 3)square
4) (2x + 3yz + w)sqare
5) (x + y - 3z)square
6) (x + y)to the 4th

please do include your solutions, I would really appreciate the helps. T_T

Answer 1

Multiply each term in the expression by the whole expression and add like terms. For example:

(x + 2y + 2z)^2 = (x + 2y + 2z)*(x + 2y + 2z)

Multiplying the first term (x) by the full expression (x + 2y + 2z) get

x^2 + 2xy + 2xz (a)

Now do the same with the second term (2y)

2xy + 4*y^2 + 4*y*z (b)

and finally the last term (2z)

2xz + 4zy + 4z^2 (c)

Then add them all [(a) + (b) + (c)] together and collect like terms.

Answer 2

Hhm perhaps you need the definition of a square, a square is an equation to the power of 2. 2 squared is 4,the square root of 4 is 2 (2*2=4). Given above the answer to number 1 is
(x + 2y + 2z)*(x + 2y + 2z) =yum alegbra!!!!!!

Answer 3

(x + 2y + 2z)^2 = x^2 + 4y^2 + 4z^2 + 4xy + 4xz + 8yz
(2x + 3y - 4z + 3w)^2 = 4x^2 + 9y^2 + 16z^2 + 9w^2 + 12xy - 16xz + 12xw - 24yz +18yx - 24zw
(x^2 - 2x + 3)^2 = x^4 + 4x^2 + 9 - 4x^3 + 6x^2 - 12x = x^4 - 4x^3 + 10x^2 - 12x + 9
(2x + 3yz + w)^2 = 4x^2 + 9y^2z^2 + w^2 + 12xyz + 4xw + 6yzw
(x + y - 3z)^2 = x^2 + y^2 + 9z^2 + 2xy -6xz - 6yz
(x + y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4

Answer 4

First, use the notation "^2" for square, "^4" for "to the 4th". It is not official, but a darn sight easier for everyone to understand, including you.

This is a question in the multiplication of polynomials by polynomials. You just have to remember that each term in the multiplier has to multiply EVERY term in the multiplicand (the guy on top). The rest is dog work. For examle, in #3,
x^2 -2x +3 multiplied by itself, will generate these terms:
with x^2: x^4-2x^3+3x^2
with -2x : -2x^3+4x^2 -6x
with +3: +3x^2-6x+9.
Just add 'em up.

PS: There is a short cut for #6, but you probably haven't got that far yet.

Answer 5

It's the same process for all of them... just expand and simplify.

(x+2y+2z)^2

= x^2 + 2xy + 2xz + 2xy + 4y^2 + 4yz + 2xz + 4yz + 4z^2

= 4y^2 + 4z^2 + x^2 + 4xy + 4xz + 8yz

...

You can do the rest =), good luck.

Answer 6

1) (x+2y+2z)(x+2y+2z)
(x^2+2xy+2xz)+(2xy+4y^2+4zy)+(2xz+4zy+4z^2)
x^2+4xy+4xz+4y^2+8zy+4z^2