expand and simplify
1.(x^2-3x+4)(-x^2+3x-4)
2.3(2x-5)-9(4x-5)
1. -x^4+3x^3-4x^2+3x^3-9x^2+12x-4x^2+12x-16
simplified form:
-x^4+6x^3-17x^2+24x-16
or
x^4-6x^3+17x^2-24x+16
2. 6x-15-36x+45
simplified form:
-30x+30
30x-30
hope it will help you. :)
To expand and simplify the given expressions, we will use the distributive property to multiply each term in the first expression by each term in the second expression, and then combine like terms.
1. (x^2 - 3x + 4)(-x^2 + 3x - 4)
First, let's multiply the first terms of each expression: (x^2) * (-x^2) = -x^4.
Next, multiply the outer terms: (x^2) * (3x) = 3x^3.
Multiply the inner terms: (-3x) * (-x^2) = 3x^3.
Multiply the last terms: (-3x) * (3x) = -9x^2.
Now, multiply the first terms of each expression in the parentheses: (x^2) * (-4) = -4x^2.
Multiply the outer terms: (x^2) * (3x) = 3x^3.
Multiply the inner terms: (-3x) * (-4) = 12x.
Finally, multiply the last terms: (-3x) * (3x) = -9x^2.
Now we can combine like terms:
Combine the x^3 terms: 3x^3 + 3x^3 = 6x^3.
Combine the x^2 terms: -9x^2 - 9x^2 - 4x^2 = -22x^2.
Combine the x terms: -4x^2 + 12x = 8x.
Combine the constant terms: -4 * (-4) = 16.
Putting it all together, the expanded and simplified expression is:
- x^4 + 6x^3 - 22x^2 + 8x + 16.
2. 3(2x - 5) - 9(4x - 5)
First, let's distribute the 3 and the 9 to each term inside their respective parentheses:
3 * 2x = 6x
3 * -5 = -15
9 * 4x = 36x
9 * -5 = -45
Now we can simplify by combining like terms:
6x - 15 - 36x + 45
Combine the x terms: 6x - 36x = -30x.
Combine the constant terms: -15 + 45 = 30.
Putting it all together, the simplified expression is:
-30x + 30.