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Advanced Practice Questions

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Try out the following questions and leave your answer's in the comments section 1.  Identify the terms in the expression:  a). 5x² - 3xy + 7 2. Determine the coefficient, variable, and constant in the term:  a). -2x³ b).  4x²y - 3xy² + 2xy - 5x²y 3.  Identify the like terms in the expression: a).  2x²y - 3xy² + 5x² - 4xy 4. Simplify the expression by combining like terms:  a). 5a²b - 2ab² + 3a²b - 4ab² 5. Add the following like terms:  a). 2x + 3x 6.  Simplify the expression:  a). 5a - 3b + 2a - 4b  b). 3x²y - 2xy² + 5x² - 4xy + 2x² c).  3 × 2x d). (3x²)² e). 2x(3x² - 4y) 7. Simplify: a). 3(x + 2) b). 2x - 3(x - 4) c).  4x(2x² - 3y) + 5(x - 2y) 8. Simplify: a).  12x⁴y³ ÷ 3x²y² b).  8x² ÷ 2x 9). Divide and simplify:  a).  (6x³y² - 9x²y) ÷ 3xy 10.Solve for x:  a).  2x + 4 = 10 b).  3x - 5 = 2x + 7 c).  2(x + 3) - 4 = 3(x - 2) + 5

Linear Equations (finding value of one unknown)

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Finding the value of a unknown   Example :  2x + 6 = 0  { take 6 to the other side of the equal sign and it change's to a negative meaning it becomes a negative-6 } 2x = 0 -6  Meaning: 2x = -6 { divide both sides with 2 so we can have x alone one side }  Meaning: 2x /2 = -6/2 x = 3  Try out:   3y + 4 = 7 p - 4 = 3p + 4

Dividing of like and unlike terms

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Dividing like and unlike terms   -Like terms and unlike terms can divide each other  Example: 6x⁴ y⁶ ÷ 3x²y³                    : 6 ÷ 3  { First we Divide the numbers }                    :Secondly { Subtract the powers of the like                       bases } x powers  = 4-2 and                     y powers  =6 - 3 Leave us with: 2x²y³ Try out:   8a³b² ÷ 4ab

Multiplying like and unlike terms

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Like terms and unlike terms can multiply each other  https://images.app.goo.gl/aSXcekgMV1YV2PU98 Example : 3 y ² × 2 y ²                     : 3 × 2 =6   ( multiply the number)                  : y ² × y ²   ( add the exponent of the like base, 2 + 2 = 4 )                  (NB!! the y or the Base  you bring it down the way it is)   Meaning : 6 y ⁴ Example: (2 x y ) ²  (everything inside the bracket is being raised to the power 2) Meaning:  (2 x y ) ²  =  2 ²    x ²    y ²                  : 4 ² x ² y ² Try out:      a).  2k² ×  - 4k⁶ b).  6x²(2x)   c).  (4ab)²

Addition and Subtraction of like terms

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  we can only add OR substrate like terms   -3x - 4x since both signs are negative we add 3 and 4 then we keep the negative sign ( -3 + -4 = -7 ) = -7x    3x + 6y - 2x + y Example :  3x + 6y - 2x + y  Identify the like terms each term take along the sign infront of it  Meaning : 3x - 2x + 6y + y               x + 7y Try out: 5p -3r + 2p - 4r               3x² + 2x - 5x² - 2x

Identifying like terms and unlike terms

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  Like terms   -terms have the same power ams and variables   Example : 2y, -6y, 4y                   2x², x²                    x²y⁴, x²y⁴ Unlike terms  -terms have powers and variables that differ  Example : 2x, 2xy, y²                   x³, x², x⁴                  2y, xy Identifying like and unlike terms 

Basic terminologies of algebra

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What  is a Term   - is made up of the coefficient, variable/unknown and constant .                    example : 3x + 6y  -   z  +  4                               3x is  One term    6y  is One term z    is One term 4  is   One term          Algebraic terms are separated by [ +,- ] How they are Seperated  2a - 3b + 5c  x  +   y  -  z x² - xy + xz Algebraic terms are joined by { ×, ÷, (brackets), fractions and √ } How they are Joined   zy × 5yz 2 ( x + 4 ) 8c²   ÷ 2c x √ 9y   content://media/external/downloads/1000153523

Expanding/Removing the brackets

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  https://images.app.goo.gl/PNp4SjayCsJHZQWq7 Example: 4(y + 5)      (4 multiple with each term in the bracket) Meaning: 4(y) { 4 multiply (y)}  and                   :4(5)   {  4 multiply  (5)}        :4(y) + 4(5)                   : 4y + 20 Example : 3b + 2(2 +b)  { use the number and sign infront of the bracket to expand out  }   Meaning:  3b + 2(2) { the +2 multiply  (2)} + 2(b) { the +2 multiply (b)}                   :3b  + 2(2) + 2(b)                   : 3b + 4 - 2b    { collect the like terms }                   : 3b - 2b + 4   { 3b and -2b are like terms }                   : b + 4