This pdf explains how to combine the like terms in algebraic expressions and simplify them with examples for better understanding.
1. Combining and Simplifying Algebraic Terms
2. Warm Up Simplify each expression 1. a²+2b+2a²+b+2c 2. 5x+6x²+3y+2x+8y+9x² 3. g+h+2g+5h+8g²
3. 7x + 4 Constant - a • Coefficient – a number that cannot number in front of a change variable. This number is multiplied by the variable. Variable – a letter or symbol that represents an unknown number.
4. x y x² a r b² • Variables are similar to species of animals. • Different species of animals can’t mate and produce (fertile) off spring. A dog and cat can’t mate and produce a dat.
5. x y x² a r b² To be able to combine like terms, the terms must: 1. Be the same variable 2. Have the same exponent 3b + 4c + 2b = 5b +4c 4x²-3c x² - 3c + 3x² =
6. z= p= g= Combine the like terms A. 4z + 6 g + 2p + 3z + 5p + 1g 4z + 3z = 7z Combine all the like terms 2p + 5p = 7p in a new algebraic expression: 6g + 1g = 7g 7z +7p + 7g
7. c= p= g= Combine the like terms A. 10c + 4 g + 5p + 15c – 12 p - 3g 10c + 15 c = 25c 5p +(-12p) = -7p Combine all the like terms in a new algebraic 4g + (-3g) = 1g expression: 25c + (-7p) +1g
8. s= p= w= Combine the like terms A. -4s - 6w + 8p + 12s – 10 p + 13w -4s + 12s = 8s 8p + (-10p) = -2pCombine all the like terms in a new algebraic -6w + 13w = 7w expression: 8s + (-2p) + 7w
9. z= b= x= • Use the distributive property and combine the like terms Combine 5x + 3x = 8x and • 3(4z + 5x + 6b + 3x) rewrite the algebraic expression. 3(4z) = 3x4 = 12z • 3(4z + 8x + 6b) 3(8x) = 3X8 = 24x 3(6) = 18b 12z + 24x + 18b
10. X= X²= y= Combine the like terms 5x + 7x² -y + 4x – 15x² + 4y + x² 5x + 4x = 9x 7x² + (-15x²) + x² = -7x² -y + 4y = 3y Combine all the like terms in a new algebraic expression:9x + (-7x²) + 3y Or 9x -7x²+3y
11. X= X²= y= y²= p= Combine the like terms: 5x y² 4x² 6y 3p 8x -9y² -3y 2x 5x + 8x + 2x = 15x y² + (-9y²) = -8y² 6y + (-3y) = 3y Combine all the like terms in a new algebraic expression: 15x - 8y² +3y + 4x² + 3p
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