Algebra Examples

$f (x) = {(7 - 8 x)}^{2}$

Step 1

Rewrite ${(7 - 8 x)}^{2}$ as $(7 - 8 x) (7 - 8 x)$ .

$f (x) = (7 - 8 x) (7 - 8 x)$

Step 2

Expand $(7 - 8 x) (7 - 8 x)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$f (x) = 7 (7 - 8 x) - 8 x (7 - 8 x)$

Step 2.2

Apply the distributive property.

$f (x) = 7 \cdot 7 + 7 (- 8 x) - 8 x (7 - 8 x)$

Step 2.3

Apply the distributive property.

$f (x) = 7 \cdot 7 + 7 (- 8 x) - 8 x \cdot 7 - 8 x (- 8 x)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $7$ by $7$ .

$f (x) = 49 + 7 (- 8 x) - 8 x \cdot 7 - 8 x (- 8 x)$

Step 3.1.2

Multiply $- 8$ by $7$ .

$f (x) = 49 - 56 x - 8 x \cdot 7 - 8 x (- 8 x)$

Step 3.1.3

Multiply $7$ by $- 8$ .

$f (x) = 49 - 56 x - 56 x - 8 x (- 8 x)$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$f (x) = 49 - 56 x - 56 x - 8 \cdot (- 8 x \cdot x)$

Step 3.1.5

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

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Step 3.1.5.1

Move $x$ .

$f (x) = 49 - 56 x - 56 x - 8 \cdot (- 8 (x \cdot x))$

Step 3.1.5.2

Multiply $x$ by $x$ .

$f (x) = 49 - 56 x - 56 x - 8 \cdot (- 8 x^{2})$

Step 3.1.6

Multiply $- 8$ by $- 8$ .

$f (x) = 49 - 56 x - 56 x + 64 x^{2}$

Step 3.2

Subtract $56 x$ from $- 56 x$ .

$f (x) = 49 - 112 x + 64 x^{2}$

Step 4