square the first term, plus twice the product of the first and the secon, then square the second.
Try all the factoring techniques that you have been taught. If none work then it is prime (cannot be factored), try looking for (1) a greatest common factor (2) special binomials ... difference of squares, difference (or sum) of cubes (3) trinomal factoring techniques (4) other polymonials look for grouping techniques.
The advantage of recognizing some special binomials is that the math can then be done much more quickly. Some of the binomials appear very frequently.
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
In math, like algebra and calculus, a product is special when it is very common and worth knowing.Some examples area:(x + y) = ax + ay (Distibutive Law)(x + y)(x − y) = x2 − y2 (Difference of 2 squares)(x + y)2 = x2 + 2xy + y2 (Square of a sum)(x − y)2 = x2 − 2xy + y2 (Square of a difference)
No. A relation is not a special type of function.
Presumably so that they can come to an informed and calculated decision.
Special product and factoring
waht are the special features a factoring company should have
Using the special products to actually multiply things is a convenient shortcut, but not absolutely essential. Those special products, however, become REALLY useful when you need to factor things. For example, if you see the difference of two squares, you can factor it quite quickly if you remember the corresponding rule.
multiply the first factor to the first term of the second factor
Try all the factoring techniques that you have been taught. If none work then it is prime (cannot be factored), try looking for (1) a greatest common factor (2) special binomials ... difference of squares, difference (or sum) of cubes (3) trinomal factoring techniques (4) other polymonials look for grouping techniques.
You start by using the difference of squares: x24 - 1 = (x12 + 1)(x12 - 1) The second term is again a difference of squares, so you can apply this special factoring once again.
The special products include: difference of the two same terms square of a binomial cube of a binomial square of a multinomial (a+b) (a^2-ab+b^2) (a-b) (a^2+ab+b^2)
look for the patterns that the special products have.
Special product is the process of combining factors to form products.
Square of BinomialsSquare of MultinomialsTwo Binomials with Like TermsSum and Difference of Two NumbersCube of BinomialsBinomial Theorem
It depends what the special product is. Common special products are: - perfect square trinomials ... x^2 + 2ax + a^2 = (x + a)^2 - difference of squares ... x^2 - y^2 = (x - y)(x + y)