1. 5(x^2 +2x-6) - 3(2+x-x^2)
2. 2x^4-5x(x^3 -y) + 2y(5x)
3.Factor 2x^5+6x4+4x^3+12x^2
4. Factor 9y^2-18y +8
Please help. Thank you!!
1.
5x^2+10x-30 - (6+3x-3x^2)
5x^2+10x-30+3x^2-3x-6
8x^2+7x-36
2. do this the same way
3.
2x^5+6x^4+4x^3+12x^2
2x^2(x^3+3x^2 + 2x+6)
now, by inspection, we have
2x^2(x^2(x+3) + 2(x+3))
to wind up with
2x^2(x^2+2)(x+3)
4. Looks like a difference of squares, but it's one off. So, tweak it a bit:
9(y^2-2y+1)-1
9(y-1)^2 - 1^2
(3(y-1)-1)(3(y-1)+1)
(3y-4)(3y-2)
1. To simplify the expression 5(x^2 + 2x - 6) - 3(2 + x - x^2), follow these steps:
Step 1: Distribute the coefficients to the terms within each parenthesis:
-> 5 * x^2 + 5 * 2x - 5 * 6 - 3 * 2 - 3 * x + 3 * x^2
Step 2: Combine like terms:
-> 5x^2 + 10x - 30 - 6 - 3x + 3x^2
Step 3: Combine similar variable terms:
-> (5x^2 + 3x^2) + (10x - 3x) + (-30 - 6)
-> 8x^2 + 7x - 36
So, the simplified form of the expression 5(x^2 + 2x - 6) - 3(2 + x - x^2) is 8x^2 + 7x - 36.
2. To simplify the expression 2x^4 - 5x(x^3 - y) + 2y(5x), follow these steps:
Step 1: Distribute the coefficients to the terms within each parenthesis:
-> 2x^4 - 5x * x^3 - 5x(-y) + 2y * 5x
Step 2: Simplify the terms:
-> 2x^4 - 5x^4 + 5xy + 10xy
Step 3: Combine like terms:
-> (2x^4 - 5x^4) + (5xy + 10xy)
-> -3x^4 + 15xy
So, the simplified form of the expression 2x^4 - 5x(x^3 - y) + 2y(5x) is -3x^4 + 15xy.
3. To factor the expression 2x^5 + 6x^4 + 4x^3 + 12x^2, follow these steps:
Step 1: Look for common factors among all terms:
-> 2(x^5 + 3x^4 + 2x^3 + 6x^2)
Step 2: Try factoring out the greatest common factor:
-> 2x^2(x^3 + 3x^2 + 2x + 6)
At this point, you have factored out the greatest common factor, but the remaining expression cannot be easily factored further using simple techniques like factoring by grouping or the difference of squares method. If you're looking for a complete factorization, you would need to use more advanced factoring techniques or tools such as factoring calculators or software.
4. To factor the expression 9y^2 - 18y + 8, follow these steps:
Step 1: Find two factors of 8 that add up to -18. In this case, the factors are -2 and -6:
-> 9y^2 - 2y - 6y + 8
Step 2: Group similar terms and factor by grouping:
-> (9y^2 - 2y) + (-6y + 8)
-> y(9y - 2) - 2(3y - 4)
In this case, the resulting factors are y(9y - 2) - 2(3y - 4). This expression cannot be factored any further using simple techniques.