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)
just do the expansion. where do you get stuck? AND THERE'S NO NEED TO USE ALL CAPS!
To determine the product of the given expressions, we will use the distributive property and the rules of multiplying binomials. Let's solve each of the expressions step by step:
1. (3Y + 4X)(3Y - 4X)
- To multiply these binomials, we use the FOIL method, which stands for First, Outer, Inner, Last. So, we multiply the first terms, the outer terms, the inner terms, and the last terms.
- (3Y + 4X)(3Y - 4X) = (3Y * 3Y) + (3Y * -4X) + (4X * 3Y) + (4X * -4X)
- Simplifying further, we get: 9Y^2 - 12XY + 12XY - 16X^2
- The middle terms (-12XY and 12XY) cancel each other out, leaving us with: 9Y^2 - 16X^2
2. (p^(1/2)Q)^2
- To square an expression, we multiply it by itself.
- (p^(1/2)Q)^2 = (p^(1/2)Q) * (p^(1/2)Q)
- Using the product rule for exponents, we get: p^(1/2 + 1/2) * Q^1 * Q^1
- Simplifying further, we have: p^1 * Q * Q = pQ^2
3. (A + BC)(2X - 4B)
- Again, we use the FOIL method to multiply these binomials.
- (A + BC)(2X - 4B) = (A * 2X) + (A * -4B) + (BC * 2X) + (BC * -4B)
- Simplifying, we get: 2AX - 4AB + 2BCX - 4BCB
- This can be further simplified as: 2AX - 4AB + 2BCX - 4B^2C
4. (X - 1)(X^2 + 2X + 3)
- Again, we use the FOIL method to multiply these binomials.
- (X - 1)(X^2 + 2X + 3) = (X * X^2) + (X * 2X) + (X * 3) + (-1 * X^2) + (-1 * 2X) + (-1 * 3)
- Simplifying, we get: X^3 + 2X^2 + 3X - X^2 - 2X - 3
- Combining like terms, we have: X^3 + X^2 + X - 3
5. (A + 2B)(-3A^2 + 2AB + 2B^2)
- Once again, we use the FOIL method to multiply these binomials.
- (A + 2B)(-3A^2 + 2AB + 2B^2) = (A * -3A^2) + (A * 2AB) + (A * 2B^2) + (2B * -3A^2) + (2B * 2AB) + (2B * 2B^2)
- Simplifying, we get: -3A^3 + 2A^2B + 2AB^2 - 6A^2B + 4AB^2 + 4B^3
- Combining like terms, we have: -3A^3 - 4A^2B + 6AB^2 + 4B^3
I hope this explanation helps you understand how to solve these multiplication problems.