Simplify (10+7x)^2

${(10 + 7 x)}^{2}$

Step 1

Rewrite ${(10 + 7 x)}^{2}$ as $(10 + 7 x) (10 + 7 x)$ .

$(10 + 7 x) (10 + 7 x)$

Step 2

Expand $(10 + 7 x) (10 + 7 x)$ using the FOIL Method.

Apply the distributive property.

$10 (10 + 7 x) + 7 x (10 + 7 x)$

Apply the distributive property.

$10 \cdot 10 + 10 (7 x) + 7 x (10 + 7 x)$

Apply the distributive property.

$10 \cdot 10 + 10 (7 x) + 7 x \cdot 10 + 7 x (7 x)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $10$ by $10$ .

$100 + 10 (7 x) + 7 x \cdot 10 + 7 x (7 x)$

Multiply $7$ by $10$ .

$100 + 70 x + 7 x \cdot 10 + 7 x (7 x)$

Multiply $10$ by $7$ .

$100 + 70 x + 70 x + 7 x (7 x)$

Rewrite using the commutative property of multiplication.

$100 + 70 x + 70 x + 7 \cdot 7 x \cdot x$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$100 + 70 x + 70 x + 7 \cdot 7 (x \cdot x)$

Multiply $x$ by $x$ .

$100 + 70 x + 70 x + 7 \cdot 7 x^{2}$

Multiply $7$ by $7$ .

$100 + 70 x + 70 x + 49 x^{2}$

Add $70 x$ and $70 x$ .

$100 + 140 x + 49 x^{2}$