DETER MINE THE PRODUCT OF THE FOLLOWING.1.(3Y+4X)(3Y-4X) 2.(p1/2Q)2 3.(A+BC)(2X-4B) 4.(X-1)(X2+2X+3) 5.(A+2B)(-3A2+2AB+2B2)
1. 9y^2 + 24yx + 16x^2
To determine the product of each expression, we can use the distributive property or apply the rules of exponents. Let's go through each expression step by step:
1. (3Y + 4X)(3Y - 4X)
To find the product, we'll use the FOIL method (First, Outer, Inner, Last).
FOIL:
First: 3Y * 3Y = 9Y^2
Outer: 3Y * -4X = -12XY
Inner: 4X * 3Y = 12XY
Last: 4X * -4X = -16X^2
Combining the terms, the product is: 9Y^2 - 12XY + 12XY - 16X^2
Simplifying further: 9Y^2 - 16X^2
2. (p^(1/2)Q)^2
We can simplify this expression by applying the exponent rule: (a * b)^n = a^n * b^n.
Therefore, (p^(1/2)Q)^2 = p^(2/2) * Q^2 = p^1 * Q^2 = pQ^2
3. (A + BC)(2X - 4B)
Using the FOIL method again:
FOIL:
First: A * 2X = 2AX
Outer: A * -4B = -4AB
Inner: BC * 2X = 2BCX
Last: BC * -4B = -4BCB
Combining the terms, the product is: 2AX - 4AB + 2BCX - 4BCB
Simplifying further: 2AX - 4AB + 2BCX - 4B^2C
4. (X - 1)(X^2 + 2X + 3)
Again, using the FOIL method:
FOIL:
First: X * X^2 = X^3
Outer: X * 2X = 2X^2
Inner: -1 * X^2 = -X^2
Last: -1 * 2X = -2X
Combining the terms, the product is: X^3 + 2X^2 - X^2 - 2X
Simplifying further: X^3 + X^2 - 2X
5. (A + 2B)(-3A^2 + 2AB + 2B^2)
Once again, using the FOIL method:
FOIL:
First: A * -3A^2 = -3A^3
Outer: A * 2AB = 2A^2B
Inner: 2B * -3A^2 = -6A^2B
Last: 2B * 2B^2 = 4B^3
Combining the terms, the product is: -3A^3 + 2A^2B - 6A^2B + 4B^3
Simplifying further: -3A^3 - 4A^2B + 4B^3
These are the products of the given expressions.