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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

1 answer

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: \[ \boxed{16y^2 + 4y - 20} \]