Write in Standard Form (4-7y)(7+4y)

$(4 - 7 y) (7 + 4 y)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Expand $(4 - 7 y) (7 + 4 y)$ using the FOIL Method.

Apply the distributive property.

$4 (7 + 4 y) - 7 y (7 + 4 y)$

Apply the distributive property.

$4 \cdot 7 + 4 (4 y) - 7 y (7 + 4 y)$

Apply the distributive property.

$4 \cdot 7 + 4 (4 y) - 7 y \cdot 7 - 7 y (4 y)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $7$ .

$28 + 4 (4 y) - 7 y \cdot 7 - 7 y (4 y)$

Multiply $4$ by $4$ .

$28 + 16 y - 7 y \cdot 7 - 7 y (4 y)$

Multiply $7$ by $- 7$ .

$28 + 16 y - 49 y - 7 y (4 y)$

Rewrite using the commutative property of multiplication.

$28 + 16 y - 49 y - 7 \cdot 4 y \cdot y$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$28 + 16 y - 49 y - 7 \cdot 4 (y \cdot y)$

Multiply $y$ by $y$ .

$28 + 16 y - 49 y - 7 \cdot 4 y^{2}$

Multiply $- 7$ by $4$ .

$28 + 16 y - 49 y - 28 y^{2}$

Subtract $49 y$ from $16 y$ .

$28 - 33 y - 28 y^{2}$

Step 4

Move $28$ .

$- 33 y - 28 y^{2} + 28$

Step 5

Reorder $- 33 y$ and $- 28 y^{2}$ .

$- 28 y^{2} - 33 y + 28$