Add and subtract the second term to the expression and factor by Grouping
m - 1 +r (1 - m) = - (r - 1) (m - 1)
ac + 2bc - ad - 2bd = (a + 2b) (c - d)
Factor This, Like The answer by Distributing You Get The Question
42m^2 - 23mn - 84n^2 = (6m + 7n) (7m - 12n)
Add and subtract the second term to the expression and factor by Grouping
2x^2n - 3x^n + 1 = (2x^n - 1) (x^n - 1)
Special Cases ( Uses Unrational Numbers )
36x^3n + 60x^2n + 25x^n = Unfactorable
b^2x+3 c - bc^4x+1 = Unfactorable
Since both of the terms are perfect cubes,
factor using the sum of cubes formula, e.g. a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Where You Substitute a = 5r and b = s
125r^3 + s^3 = (5r + s) (25r - 5rs + s^2)
Factor out p^10 out of 32p^15 + p^10
Another rule to remove one of the functions which in this case to remove one of them you minus it by 10 on both sides also 15
32p^15 + p^10 = p^10 (32p^5 + 1)
Same Situation But This time Factor 3 Out from 12 and 3
12x^8 + 3 = 3 (4x^8 + 1)
Perfect Squares Situation
Since both terms are perfect Squares (25 and 15), factor using the difference squares formula, a^2 - b^2 = (a + b) ( a - b) where a = 5y^2 + 1 and b = 5y
25y^4 - 15y^2 + 1 =(5y^2 + 5y + 1)(5y^2 - 5y + 1)
Always Mind The Signs I Have Double Checked There Are no Errors
Answers & Comments
Answer:
Add and subtract the second term to the expression and factor by Grouping
m - 1 +r (1 - m) = - (r - 1) (m - 1)
ac + 2bc - ad - 2bd = (a + 2b) (c - d)
Factor This, Like The answer by Distributing You Get The Question
42m^2 - 23mn - 84n^2 = (6m + 7n) (7m - 12n)
Add and subtract the second term to the expression and factor by Grouping
2x^2n - 3x^n + 1 = (2x^n - 1) (x^n - 1)
Special Cases ( Uses Unrational Numbers )
36x^3n + 60x^2n + 25x^n = Unfactorable
b^2x+3 c - bc^4x+1 = Unfactorable
Since both of the terms are perfect cubes,
factor using the sum of cubes formula, e.g. a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Where You Substitute a = 5r and b = s
125r^3 + s^3 = (5r + s) (25r - 5rs + s^2)
Factor out p^10 out of 32p^15 + p^10
Another rule to remove one of the functions which in this case to remove one of them you minus it by 10 on both sides also 15
32p^15 + p^10 = p^10 (32p^5 + 1)
Same Situation But This time Factor 3 Out from 12 and 3
12x^8 + 3 = 3 (4x^8 + 1)
Perfect Squares Situation
Since both terms are perfect Squares (25 and 15), factor using the difference squares formula, a^2 - b^2 = (a + b) ( a - b) where a = 5y^2 + 1 and b = 5y
25y^4 - 15y^2 + 1 = (5y^2 + 5y + 1)(5y^2 - 5y + 1)
Always Mind The Signs I Have Double Checked There Are no Errors
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