Solved on Dec 11, 2023

Multiply the expression $(x+5)(x-7)$ and simplify.

STEP 1

Assumptions
1. We are multiplying two binomials: $(x+5)$ and $(x-7)$ .
2. We will use the distributive property (also known as the FOIL method) to multiply the binomials.

STEP 2

The distributive property (FOIL method) tells us to multiply each term in the first binomial by each term in the second binomial. The acronym FOIL stands for First, Outer, Inner, Last, which refers to the position of each term in the binomials.

STEP 3

First, we multiply the first terms in each binomial.
$First: x \times x = x^2$

STEP 4

Next, we multiply the outer terms in the binomials.
$Outer: x \times (-7) = -7x$

STEP 5

Then, we multiply the inner terms in the binomials.
$Inner: 5 \times x = 5x$

STEP 6

Finally, we multiply the last terms in each binomial.
$Last: 5 \times (-7) = -35$

STEP 7

Now, we combine all the products from the previous steps.
$x^2 + (-7x) + 5x + (-35)$

STEP 8

Combine like terms. In this case, the like terms are $-7x$ and $5x$ .
$-7x + 5x = -2x$

STEP 9

Write the final expression by combining the terms from STEP_7 and STEP_8.
$x^2 - 2x - 35$
The product of the factors $(x+5)(x-7)$ is $x^2 - 2x - 35$ .

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Multiply the expression $(x+5)(x-7)$ and simplify.

STEP 1

Assumptions
1. We are multiplying two binomials: $(x+5)$ and $(x-7)$ .
2. We will use the distributive property (also known as the FOIL method) to multiply the binomials.

STEP 2

The distributive property (FOIL method) tells us to multiply each term in the first binomial by each term in the second binomial. The acronym FOIL stands for First, Outer, Inner, Last, which refers to the position of each term in the binomials.

STEP 3

First, we multiply the first terms in each binomial.
$First: x \times x = x^2$

STEP 4

Next, we multiply the outer terms in the binomials.
$Outer: x \times (-7) = -7x$

STEP 5

Then, we multiply the inner terms in the binomials.
$Inner: 5 \times x = 5x$

STEP 6

Finally, we multiply the last terms in each binomial.
$Last: 5 \times (-7) = -35$

STEP 7

Now, we combine all the products from the previous steps.
$x^2 + (-7x) + 5x + (-35)$

STEP 8

Combine like terms. In this case, the like terms are $-7x$ and $5x$ .
$-7x + 5x = -2x$

STEP 9

Write the final expression by combining the terms from STEP_7 and STEP_8.
$x^2 - 2x - 35$
The product of the factors $(x+5)(x-7)$ is $x^2 - 2x - 35$ .

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Multiply the expression (x+5)(x−7)(x+5)(x-7)(x+5)(x−7) and simplify.

STEP 1

Assumptions1. We are multiplying two binomials: (x+5)(x+5)(x+5) and (x−7)(x-7)(x−7).2. We will use the distributive property (also known as the FOIL method) to multiply the binomials.

STEP 2

The distributive property (FOIL method) tells us to multiply each term in the first binomial by each term in the second binomial. The acronym FOIL stands for First, Outer, Inner, Last, which refers to the position of each term in the binomials.

STEP 3

First, we multiply the first terms in each binomial.First:x×x=x2First: x \times x = x^2First:x×x=x2

STEP 4

Next, we multiply the outer terms in the binomials.Outer:x×(−7)=−7xOuter: x \times (-7) = -7xOuter:x×(−7)=−7x

STEP 5

Then, we multiply the inner terms in the binomials.Inner:5×x=5xInner: 5 \times x = 5xInner:5×x=5x

STEP 6

Finally, we multiply the last terms in each binomial.Last:5×(−7)=−35Last: 5 \times (-7) = -35Last:5×(−7)=−35

STEP 7

Now, we combine all the products from the previous steps.x2+(−7x)+5x+(−35)x^2 + (-7x) + 5x + (-35)x2+(−7x)+5x+(−35)

STEP 8

Combine like terms. In this case, the like terms are −7x-7x−7x and 5x5x5x.−7x+5x=−2x-7x + 5x = -2x−7x+5x=−2x

STEP 9

Write the final expression by combining the terms from STEP_7 and STEP_8.x2−2x−35x^2 - 2x - 35x2−2x−35The product of the factors (x+5)(x−7)(x+5)(x-7)(x+5)(x−7) is x2−2x−35x^2 - 2x - 35x2−2x−35.

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Multiply the expression $(x+5)(x-7)$ and simplify.

Assumptions
1. We are multiplying two binomials: $(x+5)$ and $(x-7)$ .
2. We will use the distributive property (also known as the FOIL method) to multiply the binomials.

First, we multiply the first terms in each binomial.
$First: x \times x = x^2$

Next, we multiply the outer terms in the binomials.
$Outer: x \times (-7) = -7x$

Then, we multiply the inner terms in the binomials.
$Inner: 5 \times x = 5x$

Finally, we multiply the last terms in each binomial.
$Last: 5 \times (-7) = -35$

Now, we combine all the products from the previous steps.
$x^2 + (-7x) + 5x + (-35)$

Combine like terms. In this case, the like terms are $-7x$ and $5x$ .
$-7x + 5x = -2x$

Write the final expression by combining the terms from STEP_7 and STEP_8.
$x^2 - 2x - 35$
The product of the factors $(x+5)(x-7)$ is $x^2 - 2x - 35$ .