(x-8)-x(x-6).jpeg "(x+8)(x-8)-x(x-6)")
Simplifying the Expression (x+8)(x-8)-x(x-6)
This article will guide you through the process of simplifying the algebraic expression (x+8)(x-8)-x(x-6).
Expanding the Expression
The first step is to expand the expression by multiplying out the brackets.
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(x+8)(x-8) can be expanded using the difference of squares formula: (a+b)(a-b) = a² - b². In this case, a = x and b = 8.
- Therefore, (x+8)(x-8) = x² - 8² = x² - 64.
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x(x-6) is expanded by distributing x to both terms inside the bracket.
- Therefore, x(x-6) = x² - 6x.
Now, the expression becomes: x² - 64 - (x² - 6x)
Simplifying Further
Next, we need to remove the brackets and combine like terms.
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Since there is a minus sign in front of the bracket, we need to change the signs of the terms inside the bracket.
- This gives us: x² - 64 - x² + 6x
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Now we can combine the x² terms, which cancel each other out.
- This leaves us with: -64 + 6x
Final Simplified Expression
The simplified form of the expression (x+8)(x-8)-x(x-6) is 6x - 64.
Conclusion
By expanding the brackets and simplifying the expression, we were able to express it in a much simpler form. This simplified form is easier to work with when performing further calculations or solving equations.