Solved on Feb 08, 2024

Expand the expression $(x-8)(x+2)$ using the FOIL method.

STEP 1

Assumptions
1. We are given a binomial expression $(x-8)(x+2)$ .
2. We need to use the FOIL method to expand this expression.
3. FOIL stands for First, Outer, Inner, Last, which refers to a method for multiplying two binomials.
4. The result will be a quadratic expression.

STEP 2

First, we multiply the First terms in each binomial.
$First = x \cdot x$

STEP 3

Calculate the product of the First terms.
$First = x^2$

STEP 4

Next, we multiply the Outer terms in each binomial.
$Outer = x \cdot 2$

STEP 5

Calculate the product of the Outer terms.
$Outer = 2x$

STEP 6

Now, we multiply the Inner terms in each binomial.
$Inner = -8 \cdot x$

STEP 7

Calculate the product of the Inner terms.
$Inner = -8x$

STEP 8

Finally, we multiply the Last terms in each binomial.
$Last = -8 \cdot 2$

STEP 9

Calculate the product of the Last terms.
$Last = -16$

STEP 10

Now, we combine all the products from the First, Outer, Inner, and Last steps to get the expanded form.
$Expanded\, form = First + Outer + Inner + Last$

STEP 11

Substitute the calculated products into the expanded form.
$Expanded\, form = x^2 + 2x - 8x - 16$

STEP 12

Combine like terms in the expanded form to simplify the expression.
$Expanded\, form = x^2 + (2x - 8x) - 16$

STEP 13

Simplify the like terms.
$Expanded\, form = x^2 - 6x - 16$
The expanded form of $(x-8)(x+2)$ using the FOIL method is $x^2 - 6x - 16$ .

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Expand the expression $(x-8)(x+2)$ using the FOIL method.

STEP 1

Assumptions
1. We are given a binomial expression $(x-8)(x+2)$ .
2. We need to use the FOIL method to expand this expression.
3. FOIL stands for First, Outer, Inner, Last, which refers to a method for multiplying two binomials.
4. The result will be a quadratic expression.

STEP 2

First, we multiply the First terms in each binomial.
$First = x \cdot x$

STEP 3

Calculate the product of the First terms.
$First = x^2$

STEP 4

Next, we multiply the Outer terms in each binomial.
$Outer = x \cdot 2$

STEP 5

Calculate the product of the Outer terms.
$Outer = 2x$

STEP 6

Now, we multiply the Inner terms in each binomial.
$Inner = -8 \cdot x$

STEP 7

Calculate the product of the Inner terms.
$Inner = -8x$

STEP 8

Finally, we multiply the Last terms in each binomial.
$Last = -8 \cdot 2$

STEP 9

Calculate the product of the Last terms.
$Last = -16$

STEP 10

Now, we combine all the products from the First, Outer, Inner, and Last steps to get the expanded form.
$Expanded\, form = First + Outer + Inner + Last$

STEP 11

Substitute the calculated products into the expanded form.
$Expanded\, form = x^2 + 2x - 8x - 16$

STEP 12

Combine like terms in the expanded form to simplify the expression.
$Expanded\, form = x^2 + (2x - 8x) - 16$

STEP 13

Simplify the like terms.
$Expanded\, form = x^2 - 6x - 16$
The expanded form of $(x-8)(x+2)$ using the FOIL method is $x^2 - 6x - 16$ .

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Expand the expression (x−8)(x+2)(x-8)(x+2)(x−8)(x+2) using the FOIL method.

STEP 1

Assumptions1. We are given a binomial expression (x−8)(x+2)(x-8)(x+2)(x−8)(x+2).2. We need to use the FOIL method to expand this expression.3. FOIL stands for First, Outer, Inner, Last, which refers to a method for multiplying two binomials.4. The result will be a quadratic expression.

STEP 2

First, we multiply the First terms in each binomial.First=x⋅xFirst = x \cdot xFirst=x⋅x

STEP 3

Calculate the product of the First terms.First=x2First = x^2First=x2

STEP 4

Next, we multiply the Outer terms in each binomial.Outer=x⋅2Outer = x \cdot 2Outer=x⋅2

STEP 5

Calculate the product of the Outer terms.Outer=2xOuter = 2xOuter=2x

STEP 6

Now, we multiply the Inner terms in each binomial.Inner=−8⋅xInner = -8 \cdot xInner=−8⋅x

STEP 7

Calculate the product of the Inner terms.Inner=−8xInner = -8xInner=−8x

STEP 8

Finally, we multiply the Last terms in each binomial.Last=−8⋅2Last = -8 \cdot 2Last=−8⋅2

STEP 9

Calculate the product of the Last terms.Last=−16Last = -16Last=−16

STEP 10

Now, we combine all the products from the First, Outer, Inner, and Last steps to get the expanded form.Expanded form=First+Outer+Inner+LastExpanded\, form = First + Outer + Inner + LastExpandedform=First+Outer+Inner+Last

STEP 11

Substitute the calculated products into the expanded form.Expanded form=x2+2x−8x−16Expanded\, form = x^2 + 2x - 8x - 16Expandedform=x2+2x−8x−16

STEP 12

Combine like terms in the expanded form to simplify the expression.Expanded form=x2+(2x−8x)−16Expanded\, form = x^2 + (2x - 8x) - 16Expandedform=x2+(2x−8x)−16

STEP 13

Simplify the like terms.Expanded form=x2−6x−16Expanded\, form = x^2 - 6x - 16Expandedform=x2−6x−16The expanded form of (x−8)(x+2)(x-8)(x+2)(x−8)(x+2) using the FOIL method is x2−6x−16x^2 - 6x - 16x2−6x−16.

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Expand the expression $(x-8)(x+2)$ using the FOIL method.

Assumptions
1. We are given a binomial expression $(x-8)(x+2)$ .
2. We need to use the FOIL method to expand this expression.
3. FOIL stands for First, Outer, Inner, Last, which refers to a method for multiplying two binomials.
4. The result will be a quadratic expression.

First, we multiply the First terms in each binomial.
$First = x \cdot x$

Calculate the product of the First terms.
$First = x^2$

Next, we multiply the Outer terms in each binomial.
$Outer = x \cdot 2$

Calculate the product of the Outer terms.
$Outer = 2x$

Now, we multiply the Inner terms in each binomial.
$Inner = -8 \cdot x$

Calculate the product of the Inner terms.
$Inner = -8x$

Finally, we multiply the Last terms in each binomial.
$Last = -8 \cdot 2$

Calculate the product of the Last terms.
$Last = -16$

Now, we combine all the products from the First, Outer, Inner, and Last steps to get the expanded form.
$Expanded\, form = First + Outer + Inner + Last$

Substitute the calculated products into the expanded form.
$Expanded\, form = x^2 + 2x - 8x - 16$

Combine like terms in the expanded form to simplify the expression.
$Expanded\, form = x^2 + (2x - 8x) - 16$

Simplify the like terms.
$Expanded\, form = x^2 - 6x - 16$
The expanded form of $(x-8)(x+2)$ using the FOIL method is $x^2 - 6x - 16$ .