Question

Find the product of (4y+5)(4y−4)%0D%0A(%0D%0A4%0D%0A%0D%0A+%0D%0A5%0D%0A)%0D%0A(%0D%0A4%0D%0A%0D%0A−%0D%0A4%0D%0A)%0D%0Ain standard form. You can use the Algebra tiles to help you.(1 point)%0D%0AResponses%0D%0A%0D%0A−16y2+20y−4%0D%0A−%0D%0A16%0D%0A%0D%0A2%0D%0A+%0D%0A20%0D%0A%0D%0A−%0D%0A4%0D%0Anegative 16 y squared plus 20 y minus 4%0D%0A%0D%0A8y+1%0D%0A8%0D%0A%0D%0A+%0D%0A1%0D%0A8 y plus 1%0D%0A%0D%0A−20+4y+16y2%0D%0A−%0D%0A20%0D%0A+%0D%0A4%0D%0A%0D%0A+%0D%0A16%0D%0A%0D%0A2%0D%0Anegative 20 plus 4 y plus 16 y squared%0D%0A%0D%0A16y2+4y−20

Answer 1

To find the product of \( (4y + 5)(4y - 4) \), we can use the distributive property (also known as FOIL for binomials).

Here’s how it works step by step:

1. **First:** Multiply the first terms:
\[
4y \cdot 4y = 16y^2
\]

2. **Outer:** Multiply the outer terms:
\[
4y \cdot (-4) = -16y
\]

3. **Inner:** Multiply the inner terms:
\[
5 \cdot 4y = 20y
\]

4. **Last:** Multiply the last terms:
\[
5 \cdot (-4) = -20
\]

Now, we combine all these products together:
\[
16y^2 - 16y + 20y - 20
\]

Now combine the like terms \(-16y + 20y\):
\[
16y^2 + 4y - 20
\]

Thus, the product of \( (4y + 5)(4y - 4) \) in standard form is:
\[
\boxed{16y^2 + 4y - 20}
\]