%2B(x%5E2-x-27)-(x%2B5)(x-7).jpeg "(4x^2+8x+15)+(x^2-x-27)-(x+5)(x-7)")
Simplifying the Expression: (4x^2+8x+15)+(x^2-x-27)-(x+5)(x-7)
This article will guide you through the process of simplifying the given expression: (4x^2+8x+15)+(x^2-x-27)-(x+5)(x-7).
Step 1: Expand the Product
Begin by expanding the product of the binomials: (x+5)(x-7). This is done using the FOIL method (First, Outer, Inner, Last):
(x+5)(x-7) = xx + x(-7) + 5x + 5(-7) = x^2 - 7x + 5x - 35 = x^2 - 2x - 35
Step 2: Substitute and Combine Like Terms
Now, substitute the expanded product back into the original expression:
(4x^2+8x+15)+(x^2-x-27) - (x^2 - 2x - 35)
Next, remove the parentheses and combine like terms:
4x^2 + 8x + 15 + x^2 - x - 27 - x^2 + 2x + 35
= (4x^2 + x^2 - x^2) + (8x - x + 2x) + (15 - 27 + 35)
Step 3: Simplify
Finally, simplify the expression:
= 4x^2 + 9x + 23
Therefore, the simplified form of the given expression is 4x^2 + 9x + 23.