## 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.