(ax-1)-x%5E2%2B4.jpeg "(4x+4)(ax-1)-x^2+4")
Expanding and Simplifying the Expression (4x+4)(ax-1)-x^2+4
This article will guide you through the process of expanding and simplifying the algebraic expression (4x+4)(ax-1)-x^2+4.
Step 1: Expanding the Product
We begin by expanding the product of the two binomials: (4x+4)(ax-1). This is done using the distributive property or the FOIL method.
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Using Distributive Property:
- Multiply each term in the first binomial by each term in the second binomial:
- (4x)(ax) + (4x)(-1) + (4)(ax) + (4)(-1)
- Multiply each term in the first binomial by each term in the second binomial:
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Using FOIL Method:
- Multiply the First terms: (4x)(ax) = 4ax²
- Multiply the Outer terms: (4x)(-1) = -4x
- Multiply the Inner terms: (4)(ax) = 4ax
- Multiply the Last terms: (4)(-1) = -4
Combining both methods, we get the expanded expression: 4ax² - 4x + 4ax - 4
Step 2: Combining Like Terms
Now, we combine the terms with the same variable and exponent:
4ax² - 4x + 4ax - 4 = 4ax² + (4a - 4)x - 4
Step 3: Incorporating the Remaining Terms
Finally, we add the remaining terms from the original expression: -x² + 4. This results in the final simplified expression:
4ax² + (4a - 4)x - 4 - x² + 4 = (4a - 1)x² + (4a - 4)x
Conclusion
By expanding the product, combining like terms, and incorporating the remaining terms, we have successfully simplified the expression (4x+4)(ax-1)-x^2+4 into (4a - 1)x² + (4a - 4)x. This simplified form is easier to work with and understand.