(%E2%88%92b2%2B7).jpeg "(b2+5)(−b2+7)")
Expanding the Expression (b² + 5)(-b² + 7)
This article will guide you through the process of expanding the expression (b² + 5)(-b² + 7) using the distributive property, also known as FOIL (First, Outer, Inner, Last).
Understanding the FOIL Method
FOIL is a mnemonic acronym that helps remember the steps for multiplying two binomials:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of the binomials.
- Inner: Multiply the inner terms of the binomials.
- Last: Multiply the last terms of each binomial.
Expanding the Expression
Let's apply FOIL to our expression:
- First: (b²) (-b²) = -b⁴
- Outer: (b²) (7) = 7b²
- Inner: (5) (-b²) = -5b²
- Last: (5) (7) = 35
Now, we combine the terms:
-b⁴ + 7b² - 5b² + 35
Finally, simplify by combining like terms:
-b⁴ + 2b² + 35
Conclusion
By applying the FOIL method, we have successfully expanded the expression (b² + 5)(-b² + 7) to -b⁴ + 2b² + 35. Remember, FOIL is a helpful tool for expanding any binomial multiplication.