Smart Math in Multiplication  Algebra ShapeNote back in shape algebra distributive properties. Distributive propertiesis the basic concept of multiplication in the algebra. For more details,learned the following description.The multiplication rate with Two PartsIn order for you to understand the multiplication rate of the two-rate form of algebra,learn about the following example. 

Use the distributive law to complete the following multiplication.a. 2 (x + 3)
b. -5 (9 - y) 

c. 3x (y + 5)

d. -9p (5p - 2q)Answer:a. 2 (x + 3) = 2x + 6
b. -5 (9 - y) + 5y = -45
c. 3x (y + 5) = 3xy + 15x

d. -9p (5p - 2q) =-45p2 + 18pq

Smart Math in factoring with Distributive Properties In elementary school, you would have learned how factoring a numbers. Remember you regarding the matter? Basically,factoring a number means a number expressed inform of multiplication factors. In this section, will be studied in ways factoring an algebraic form by using the distributive properties.With these properties, the form ax + ay algebra can be factored into a (x + y),where a is a factor of ax and ay fellowship. Therefore, study 

Example Problem 

Factor the following algebraic forms.a. 5ab 10b + c. +-15p2q2 10pqb. 2x - 8x2yAnswer:a. 10b + 5abFor factoring 5ab + 10b, specify fellowship factor of 5 and10, then from ab and b. Fellowship factor of 5 and 10 is 5.Factors fellowship of ab and b is b.So, 5ab factored into 5b 10b + (a + 2).b. 2x - 8x2y  

Fellowship factor of 2 and -8 is 2.Factor of x and x2y fellowship is x.Thus, 2x - 8x2y = 2x (1 - 4xy).c. +-15p2q2 10pqFactors fellowship of -15 and 10 is 5.Factors fellowship of p2q2 and pq is pq.So-15p2q2 10pq + = 5pq (-3pq + 2). 

Smart Math in Difference Two Squares Notice the multiplication (a + b) (a - b). This form can be written(a + b) (a - b) = a² - ab + ab - b ²= a² - b ²So, the form a2 - b2 can be expressed in terms of multiplication (a + b) (a - b).a² - b² = (a + b) (a - b)Forms a² - b ² is called the difference of two squares.Factor the following forms.a. p² - 4c. 16 m² - 9N ²b. 25x² - y ²d. 20p² - 5q²Answer:a. p2 - 4 = (p + 2) (p - 2)b. 25x² - y² = (5x + y) (5x - y)c. 16m2 - 9n2 = (4m + 3n) (4m - 3n)d. 20p ² - 5q ² = 5 (4p ² - q ²) = 5 (2p + q) (2p - q) 

Smart Math in factoring quadratic form ax ² + bx + c with a = 1Note the multiplication of the following two parts.(X + p) (x + q) = x² + px + qx + pq= X² + (p + q) x + pq So, the form x² + (p + q) x + pq can be factored into (x + p) (x + q).Supose, x² + (p + q) x + pq = ax ² + bx + c so a = 1, b = p + q,and c = pq.Of the example, it can be seen that p and q are factors of c. If p and q are summed, the result is b. Thus for factoring the form ax ² + bx + c with a = 1, specify two numbers a factor of c and if the two numbers are added together,the result is the same as b.So that you may better understand the material, study the following example problems:

Fraction following forms.

• a.) x² + 5x + 6 
• b.) ax ² + 2x - 8

Answer:a. x ² + 5x + 6 = (x + ...) (x + ...)Suppose, x ² + 5x + 6 = ax2 + bx + c, obtained a = 1, b = 5, and c = 6.To fill in the blank, specify two numbers is a factor of 6and if the two numbers are added together, the result is equal to 5.Factor of 6 is 6 and 1 or 2 and 3, which is 2 and a qualified So, x ² + 5x + 6 = (x + 2) (x + 3) 

b. x2 + 2x - 8 = (x + ...) (x + ...)By way as in (a), obtained by a = 1, b = 2, and c = -8.Factors of 8 are 1, 2, 4, and 8. Therefore c = -8, one of the two numbers is sought must be negative. Thus, the two Eligible numbers are -2 and 4, because -2 × 4 = -8 and-2 + 4 = 2.So, x ² + 2x - 8 = (x + (-2)) (x + 4) = (x - 2) (x + 4)Factoring Form ax ² + bx + c with a ≠ 1Previously, you had factored form ax2 + bx + c with a = 1.Now you will learn how to factor in the form ax2 + bx + c with a ≠ 1.Note the multiplication of the following two parts.(X + 3) (2x + 1) = 2x + x ² + 6x + 3= 2x ² + 7x + 3In other words, the form 2x2 + 7x + 3 be factored into (x + 3) (2x + 1).As for how factoring 2x ² + 7x + 3 is the reverse phase binomial multiplication above.2x ² + 7x + 3 = 2x ² + (x + 6 x) +3= (2x ² + x) + (6x + 3)= X (2x + 1) + 3 (2x + 1)= (X + 3) (2x +1)

From the description you can know how to factor in the forma x ² + bx + c with a ≠ 1 as follows.1) Describe bx be the sum of the two tribes that if the two tribes    The same result multiplied by (ax ²) (c).2) Factor the form obtained using distributive properties

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