DISTRIBUTIVE PROPERTY AND COLLECTING LIKE TERMS - Daily Math Guide
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## DISTRIBUTIVE PROPERTY AND COLLECTING LIKE TERMS

Distributive property is the opposite of factoring. In this rule, the outsider "a" was distributed inside the parenthesis to multiply "x" and "y". The "a" then is with the "x", and "y" as well, as products. The rule is simple to follow since you just have to check where the position of "a" as its behavior will be the basis of

different  distributive problems arises. The photo shows the pattern of "a" . Following the pattern will easy as constant practice will be applied. The illustrations below was provided to have a better understanding about this simple Algebraic properties.

Illustrative example:

Find the output by using distributive property:

Given:

3(a + 5)

Let us assign values found in the photo provided. Where "a=3", "x=a", and "y=5". Following the pattern, it shows that "3(a+5)= 3 a+ 3*5 = 3 a+ 15", (* means multiply). On the next example, it is by intention that it was made with a little twist on the "x & y" part.

Given:

4(3x - 2y )

Again by the same structure, "a=4", "x=3x", and "y=2y". y applying the same principle, te expression will arrived to "4(3x - 2y )=12x - 8y".

Given:

$4(\frac{x}{2}+2)=$

Case like this, fraction plays for "x" in the pattern so, our "a = 4", "x = x/2", and "y=2". So, the resulting output would be ;

$4(\frac{x}{2}+2)=2x+8$

Provided below were answered problem to gain more scenarios about the subject matter.

Perform the Algebraic property and collect like terms if applicable:

$1.) 2(4-a)= {\color{Red} 8-2a}$

$2.) -5(b-4)=-5b+20={\color{Red} 20-5b}$

$3.) 4(3a-5 + a)=12a-20+4a= {\color{Red} 16a-20}$

$4.) 3a(2-b+5)=6a-3ab+15a={\color{Red} 21a-3ab}$

$5.) -3m(5n-2+1)=-15mn+6m-3m={\color{Red} 6m-15mn-3m }$

$6.) 5(2a+3b-5c)={\color{Red} 10a+15b-25c}$

$7.) 15{\color{Red} -3}(6a+3b+4)=15-18a-9b-12={\color{Red} 3-18a-9b}$

$8.){\color{Red} 2}(2x-4y+5)-7=4x-8y+10-7={\color{Red} 4x-8y+3}$

$9.) 3s(2-t+4+q-3)= 6s-3st+12s+3sq-9s={\color{Red} 9s+3sq-3st}$

$10.) 2x^{2}(\frac{2}{x}-4)={\color{Red} 4x-8x^{2}}$

Extra exercises:

$a.) -6(2a-3b)={\color{Red} ?}$

$b.) 4(2-5c+3)={\color{Red} ?}$

$c.) a+3(5a-4)={\color{Red} ?}$

## REFERENCE

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