Simplify (2w+7x-4)(7w+5+2)

$(2 w + 7 x - 4) (7 w + 5 + 2)$

Step 1

Add $5$ and $2$ .

$(2 w + 7 x - 4) (7 w + 7)$

Step 2

Expand $(2 w + 7 x - 4) (7 w + 7)$ by multiplying each term in the first expression by each term in the second expression.

$2 w (7 w) + 2 w \cdot 7 + 7 x (7 w) + 7 x \cdot 7 - 4 (7 w) - 4 \cdot 7$

Step 3

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 7 w \cdot w + 2 w \cdot 7 + 7 x (7 w) + 7 x \cdot 7 - 4 (7 w) - 4 \cdot 7$

Multiply $w$ by $w$ by adding the exponents.

Move $w$ .

$2 \cdot 7 (w \cdot w) + 2 w \cdot 7 + 7 x (7 w) + 7 x \cdot 7 - 4 (7 w) - 4 \cdot 7$

Multiply $w$ by $w$ .

$2 \cdot 7 w^{2} + 2 w \cdot 7 + 7 x (7 w) + 7 x \cdot 7 - 4 (7 w) - 4 \cdot 7$

Multiply $2$ by $7$ .

$14 w^{2} + 2 w \cdot 7 + 7 x (7 w) + 7 x \cdot 7 - 4 (7 w) - 4 \cdot 7$

Multiply $7$ by $2$ .

$14 w^{2} + 14 w + 7 x (7 w) + 7 x \cdot 7 - 4 (7 w) - 4 \cdot 7$

Rewrite using the commutative property of multiplication.

$14 w^{2} + 14 w + 7 \cdot 7 x w + 7 x \cdot 7 - 4 (7 w) - 4 \cdot 7$

Multiply $7$ by $7$ .

$14 w^{2} + 14 w + 49 x w + 7 x \cdot 7 - 4 (7 w) - 4 \cdot 7$

Multiply $7$ by $7$ .

$14 w^{2} + 14 w + 49 x w + 49 x - 4 (7 w) - 4 \cdot 7$

Multiply $7$ by $- 4$ .

$14 w^{2} + 14 w + 49 x w + 49 x - 28 w - 4 \cdot 7$

Multiply $- 4$ by $7$ .

$14 w^{2} + 14 w + 49 x w + 49 x - 28 w - 28$

Simplify by adding terms.

Subtract $28 w$ from $14 w$ .

$14 w^{2} - 14 w + 49 x w + 49 x - 28$

Simplify the expression.

Move $x$ .

$14 w^{2} - 14 w + 49 w x + 49 x - 28$

Move $- 14 w$ .

$14 w^{2} + 49 w x + 49 x - 14 w - 28$

Reorder $14 w^{2}$ and $49 w x$ .

$49 w x + 14 w^{2} + 49 x - 14 w - 28$