Help Please:
Please Help
1.Essay:Show all work,Find the Product.
(x^2-2)(x^3-4x+9)
2.Find the product:(2x-4y)(2x+4y)
4.Find the product:(8x-3y)^2
a.64x^2+9y^2
b.64x^2-9y^2
c.64x^2-48xy+9y^2
d.64x^2-48xy-9y^2 (b)
(x^2 -2)(x^3 - 4x + 9)
(x^2) (x^3) = x^5
(x^2) (-4x) = -4x^3
(x^2) (9) = 9x^2
(-2) (x^3) = -2x^3
(-2) (-4x) = 8x
(-2) (9) = 18
Now, we add the right-hand sides of the equeal sign.
x^5 - 4x^3 - 2x^3 + 9x^2 + 8x - 18
x^5 - 6x^3 + 9x^2 + 8x - 18
There I did the 1st one for u. Try and do the rest.
(2x-4y)(2x+4y)
4x^2 + 8xy - 8xy - 16y^2
4x^2 - 16y2
(8x-3y)^2
(8x - 3y) (8x - 3y)
Try finish it from there...
Thanks Priya and Mithra I appreciate your help.
Sure! I'll explain how to find the product for each question.
1. Essay: To find the product of the expression (x^2-2)(x^3-4x+9), we need to use the distributive property, which states that we must multiply each term in the first expression by each term in the second expression. Here's how to do it step by step:
- Multiply the first term in the first expression (x^2) by each term in the second expression (x^3, -4x, and 9):
(x^2 * x^3) = x^(2+3) = x^5 (using the rule of exponents)
(x^2 * -4x) = -4x^(2+1) = -4x^3
(x^2 * 9) = 9x^2
- Now, multiply the second term in the first expression (-2) by each term in the second expression:
(-2 * x^3) = -2x^3
(-2 * -4x) = 8x
(-2 * 9) = -18
- Finally, combine all the terms obtained above:
x^5 - 4x^3 + 9x^2 - 2x^3 + 8x - 18
And that is the product of the given expression.
2. To find the product (2x-4y)(2x+4y), we can use the formula for multiplying two binomials, which is FOIL (First, Outer, Inner, Last). Here's how to do it step by step:
- Multiply the first terms of each binomial:
(2x * 2x) = 4x^2
- Multiply the outer terms of each binomial:
(2x * 4y) = 8xy
- Multiply the inner terms of each binomial:
(-4y * 2x) = -8xy
- Multiply the last terms of each binomial:
(-4y * 4y) = -16y^2
- Finally, combine all the terms obtained above:
4x^2 + 8xy - 8xy - 16y^2
Simplifying further, we get:
4x^2 - 16y^2
So, the product of (2x-4y)(2x+4y) is 4x^2 - 16y^2.
4. To find the product of (8x-3y)^2, we need to square the entire expression. This means multiplying the expression by itself. Here's how to do it step by step:
- Multiply the expression (8x-3y) by itself:
(8x-3y) * (8x-3y)
Using the FOIL method mentioned earlier, we can expand this expression as follows:
(8x * 8x) = 64x^2
(8x * -3y) = -24xy
(-3y * 8x) = -24xy
(-3y * -3y) = 9y^2
Combining all the terms obtained above, we get:
64x^2 - 24xy - 24xy + 9y^2
Simplifying further, we obtain:
64x^2 - 48xy + 9y^2
Therefore, the product of (8x-3y)^2 is 64x^2 - 48xy + 9y^2, which matches option (c).
I hope this helps! Let me know if you have any other questions.