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How do you factor b2 - 7b plus 12?
b^2 - 7b + 12 = b^2 - 4b - 3b + 12 = b(b -4) -3(b - 4) = (b - 3)(b - 4)
Why isnt subtraction commutative?
Example: a - b = b-a, So lets say a=2 b=3. 2-3=3-2 -1 =/= 1
Does a plus b plus 2 plus 3 equals 2a plus 3b?
a+b+2+3=5+a+b
Is a to the second power over b to the second power greater than a over b?
Let's reverse the question - Is a over b less than a squared over b squared? Answer - Only when a is less than b example 1: a is less than b a = 2 a squared = 4 b = 3 b squared = 9 2 / 3 = .6666 4 / 9 = .444444 2 / 3 is greater than 4 / 9 example 2: a is equal to b a = 2 a squared = 4 b = 2 b squared = 4 2 / 4 = .5 2 / 4 = .5 2 / 4 is equal to 2 / 4 example 3: a is greater than b a = 3 a squared = 9 b = 2 b squared = 4 3 / 2 = 1.5 9 / 4 = 2.25 3 / 2 is less than 9 / 4 - wjs1632 -
the ratio of A to B is 2:3 and the ratio of B to C is 4:5. what is the ratio of A to C?
This deals with ratios and proportions. ⊱ ────── ✯ ────── ⊰ A : B = 2 : 3 B : C = 4 : 5. Now, to find A : B : C, we need to make the value of B equal in A : B ratio and B : C ratio. Here, Value of B in A : B ratio is 3; and B : C ratio is 4. LCM of 3 and 4 is 12. Therefore, we multiply 4 to the first ratio and 3 to the second ratio. A : B = 2 × 4 : 3 × 4 A : B = 8 : 12 Also, B : C = 4 × 3 : 5 × 3 B : C = 12 : 15 Now, we can combine A : B and B : C. A : B : C = 8 : 12 : 15.
Algebraic expression a cubed minuis B-Cubed?
a^(3) - b^(-3) = a^(3) - 1/b^(3) This factors to (a - 1/b)(a^2 + a/b + (1/b)^2))
What is the Definition of Factoring sum or difference of two cubes?
a^3 + b^3 = (a + b)(a^2 - ab + b^2) a^3 - b^3 = (a - b)(a^2 + ab + b^2)
What are the different special product formulas?
1. Square of a binomial (a+b)^2 = a^2 + 2ab + b^2 carry the signs as you solve 2. Square of a Trinomial (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc carry the sings as you solve 3. Cube of a Binomial (a+b)^3 = a^3 + 3(a^2)b + 3a(b^2) + b^3 4. Product of sum and difference (a+b)(a-b) = a^2 - b^2 5. Product of a binomial and a special multinomial (a+b)(a^2 - ab + b^2) = a^3-b^3 (a-b)(a^2 + ab + b^2) = a^3-b^3
What are the similarities of commutative and associative properties?
Conmutative: a + b = b + a 5 + 2 = 2 + 5 (a)(b) = (b)(a) (2)(3) = (3)(2) Associative: (a + b) + c = a + (b + c) (1 + 2) + 3 = 1 + (2 + 3)
How do you use distibutive property with two variables and one number?
3*(a + b) = 3*a + 3*b or a*(b + 2) = a*b + a*2
What is a cube plus b cube equal to?
It is equal to a^3 + b^3. It can also be expressed as (a + b)*(a^2 - ab + b^2) or (a^6 - b^6)/(a^3 - b^3) or many other expressions.
What are types of special product?
In mathematics, special products are of the form:(a+b)(a-b) = a2 - b2 (Product of sum and difference of two terms) which can be used to quickly solve multiplicationsuch as:301 * 299 = (300 +1)(300-1) = 3002 - 12 = 90000 - 1 = 89999types1. Square of a binomial(a+b)^2 = a^2 + 2ab + b^2carry the signs as you solve2. Square of a Trinomial(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bccarry the sings as you solve3. Cube of a Binomial(a+b)^3 = a^3 + 3(a^2)b + 3a(b^2) + b^34. Product of sum and difference(a+b)(a-b) = a^2 - b^25. Product of a binomial and a special multinomial(a+b)(a^2 - ab + b^2) = a^3-b^3(a-b)(a^2 + ab + b^2) = a^3-b^3
What are the different types of special products?
In mathematics, special products are of the form:(a+b)(a-b) = a2 - b2 (Product of sum and difference of two terms) which can be used to quickly solve multiplicationsuch as:301 * 299 = (300 +1)(300-1) = 3002 - 12 = 90000 - 1 = 89999types1. Square of a binomial(a+b)^2 = a^2 + 2ab + b^2carry the signs as you solve2. Square of a Trinomial(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bccarry the sings as you solve3. Cube of a Binomial(a+b)^3 = a^3 + 3(a^2)b + 3a(b^2) + b^34. Product of sum and difference(a+b)(a-b) = a^2 - b^25. Product of a binomial and a special multinomial(a+b)(a^2 - ab + b^2) = a^3-b^3(a-b)(a^2 + ab + b^2) = a^3-b^3
What are the types of special products?
In mathematics, special products are of the form:(a+b)(a-b) = a2 - b2 (Product of sum and difference of two terms) which can be used to quickly solve multiplicationsuch as:301 * 299 = (300 +1)(300-1) = 3002 - 12 = 90000 - 1 = 89999types1. Square of a binomial(a+b)^2 = a^2 + 2ab + b^2carry the signs as you solve2. Square of a Trinomial(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bccarry the sings as you solve3. Cube of a Binomial(a+b)^3 = a^3 + 3(a^2)b + 3a(b^2) + b^34. Product of sum and difference(a+b)(a-b) = a^2 - b^25. Product of a binomial and a special multinomial(a+b)(a^2 - ab + b^2) = a^3-b^3(a-b)(a^2 + ab + b^2) = a^3-b^3
What types of special product?
In mathematics, special products are of the form:(a+b)(a-b) = a2 - b2 (Product of sum and difference of two terms) which can be used to quickly solve multiplicationsuch as:301 * 299 = (300 +1)(300-1) = 3002 - 12 = 90000 - 1 = 89999types1. Square of a binomial(a+b)^2 = a^2 + 2ab + b^2carry the signs as you solve2. Square of a Trinomial(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bccarry the sings as you solve3. Cube of a Binomial(a+b)^3 = a^3 + 3(a^2)b + 3a(b^2) + b^34. Product of sum and difference(a+b)(a-b) = a^2 - b^25. Product of a binomial and a special multinomial(a+b)(a^2 - ab + b^2) = a^3-b^3(a-b)(a^2 + ab + b^2) = a^3-b^3
What are different types of special product?
In mathematics, special products are of the form:(a+b)(a-b) = a2 - b2 (Product of sum and difference of two terms) which can be used to quickly solve multiplicationsuch as:301 * 299 = (300 +1)(300-1) = 3002 - 12 = 90000 - 1 = 89999types1. Square of a binomial(a+b)^2 = a^2 + 2ab + b^2carry the signs as you solve2. Square of a Trinomial(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bccarry the sings as you solve3. Cube of a Binomial(a+b)^3 = a^3 + 3(a^2)b + 3a(b^2) + b^34. Product of sum and difference(a+b)(a-b) = a^2 - b^25. Product of a binomial and a special multinomial(a+b)(a^2 - ab + b^2) = a^3-b^3(a-b)(a^2 + ab + b^2) = a^3-b^3
What are the rules on factoring polynomials with common monomial?
In order to successfully factor you should follow these steps: 1.) Take out the GCF (ALWAYS DO THIS FIRST) 2.) Diff of Perfect Squares a^2-b^2=(a+b)(a-b) 3.) Diff/Sum of Cubes a^3+b^3=(a+b)(a^2-ab+b^2) a^3-b^3=(a-b)(a^2+ab+b^2) 4.) Key Number 5.) Grouping
