Lesson Example Discussion Quiz: Class Homework |
Example |
Title: Simplify the expression |
Grade: 9-a Lesson: S2-L3 |
Explanation: The best way to understand algebra is by looking at some examples. Take turns and read each example for easy understanding. |
Examples:
1. Expand \$(3b + 2c)^3 - (b - c)^2\$.
Step 1a
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Given polynomial. |
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Explanation:
Given polynomial is \$(3b + 2c)^3 - (b - c)^2\$ |
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Step 1b
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Expand polynomial by using algebraic identities. |
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Explanation: \$(3b + 2c)^3 - (b - c)^2\$ By using algebraic identity \$(a + b)^3 = a^3 + b^3 + 3ab(a + b)\$ expand polynomial \$(3b + 2c)^3 - (b - c)^2\$ \$(27b^3 + 8c^3 + 3(3b)(2c)(3b+ 2c))- (b - c)^2\$ \$(27b^3 + 8c^3 + 18bc(3b + 2c)) - (b - c)^2\$ \$(27b^3 + 8c^3 + 54b^2c + 36c^2b) - (b - c)^2\$ By using algebraic identity \$(a - b)^2 = a^2 - 2ab + b^2\$ expand polynomial \$(27b^3 + 8c^3 + 54b^2c + 36c^2b) - (b^2 -2bc + c^2)\$ \$27b^3 + 8c^3 + 54b^2c + 36c^2b - b^2 + 2bc - c^2\$ \$∴ (3b + 2c)^3 - (b - c)^2 = 27b^3 + 8c^3 + 54b^2c + 36c^2b - b^2 + 2bc - c^2\$ |
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