Simplify the expression where possible.
(x 2y 3z 4) 2
To simplify the expression (x^2y^3z^4)^2, we apply the exponent of 2 to each term inside the parentheses.
(x^2)^2 * (y^3)^2 * (z^4)^2
Simplifying each term:
(x^2)^2 = x^(2*2) = x^4
(y^3)^2 = y^(3*2) = y^6
(z^4)^2 = z^(4*2) = z^8
Putting it all together:
(x^2y^3z^4)^2 = x^4 * y^6 * z^8
To simplify the expression (x 2y 3z 4) 2, we need to square each term inside the parentheses.
(x 2y 3z 4) 2 = (x 2y 3z 4) × (x 2y 3z 4)
To multiply the terms inside the parentheses, we can use the distributive property of multiplication. We multiply each term from the first set of parentheses with every term from the second set of parentheses.
(x 2y 3z 4) × (x 2y 3z 4) = x × x + x × 2y + x × 3z + x × 4
+ 2y × x + 2y × 2y + 2y × 3z + 2y × 4
+ 3z × x + 3z × 2y + 3z × 3z + 3z × 4
+ 4 × x + 4 × 2y + 4 × 3z + 4 × 4
Now we can simplify each term by multiplying. Keep in mind that like terms can be combined.
x × x = x^2
x × 2y = 2xy
x × 3z = 3xz
x × 4 = 4x
2y × x = 2yx = 2xy
2y × 2y = 4y^2
2y × 3z = 6yz
2y × 4 = 8y
3z × x = 3zx = 3xz
3z × 2y = 6zy = 6yz
3z × 3z = 9z^2
3z × 4 = 12z
4 × x = 4x
4 × 2y = 8y
4 × 3z = 12z
4 × 4 = 16
Therefore, the simplified expression is:
x^2 + 2xy + 3xz + 4x + 4xy + 4y^2 + 6yz + 8y + 3xz + 6yz + 9z^2 + 12z + 4x + 8y + 12z + 16
We can also simplify it further by combining like terms:
x^2 + 6xy + 6xz + 8x + 4y^2 + 12yz + 16 + 9z^2
If the outside number is a power of 2, that says write the brackets out twice
(x^2y^3x^4)(x^2y^3x^4)
now since the bases are the same add up the powers.
x^(2+2)Y^(3+3) etc
= x^4y^6 etc...