Solved on Jan 23, 2024

Multiply $(8-y)(8+y)$ and simplify the result.

STEP 1

Assumptions
1. We need to multiply the two binomials: $(8-y)$ and $(8+y)$ .
2. We will use the distributive property (also known as the FOIL method) to expand the product of these two binomials.

STEP 2

The distributive property states that for any real numbers $a$ , $b$ , and $c$ :
$(a + b)(c + d) = ac + ad + bc + bd$
We will apply this property to the given binomials.

STEP 3

Identify the terms in the binomials that will be multiplied together:
First terms: $8$ and $8$ . Outer terms: $8$ and $y$ . Inner terms: $-y$ and $8$ . Last terms: $-y$ and $y$ .

STEP 4

Multiply the first terms:
$First\, terms = 8 \times 8$

STEP 5

Multiply the outer terms:
$Outer\, terms = 8 \times y$

STEP 6

Multiply the inner terms:
$Inner\, terms = -y \times 8$

STEP 7

Multiply the last terms:
$Last\, terms = -y \times y$

STEP 8

Calculate the products from steps 4 to 7:
$First\, terms = 8 \times 8 = 64$ $Outer\, terms = 8 \times y = 8y$ $Inner\, terms = -y \times 8 = -8y$ $Last\, terms = -y \times y = -y^2$

STEP 9

Combine the products:
$64 + 8y - 8y - y^2$

STEP 10

Notice that $8y$ and $-8y$ are like terms and will cancel each other out:
$64 + 8y - 8y - y^2 = 64 - y^2$

STEP 11

We have simplified the expression to:
$64 - y^2$
This is the final simplified form of the product of the two binomials $(8-y)(8+y)$ .

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Multiply $(8-y)(8+y)$ and simplify the result.

STEP 1

Assumptions
1. We need to multiply the two binomials: $(8-y)$ and $(8+y)$ .
2. We will use the distributive property (also known as the FOIL method) to expand the product of these two binomials.

STEP 2

The distributive property states that for any real numbers $a$ , $b$ , and $c$ :
$(a + b)(c + d) = ac + ad + bc + bd$
We will apply this property to the given binomials.

STEP 3

Identify the terms in the binomials that will be multiplied together:
First terms: $8$ and $8$ . Outer terms: $8$ and $y$ . Inner terms: $-y$ and $8$ . Last terms: $-y$ and $y$ .

STEP 4

Multiply the first terms:
$First\, terms = 8 \times 8$

STEP 5

Multiply the outer terms:
$Outer\, terms = 8 \times y$

STEP 6

Multiply the inner terms:
$Inner\, terms = -y \times 8$

STEP 7

Multiply the last terms:
$Last\, terms = -y \times y$

STEP 8

Calculate the products from steps 4 to 7:
$First\, terms = 8 \times 8 = 64$ $Outer\, terms = 8 \times y = 8y$ $Inner\, terms = -y \times 8 = -8y$ $Last\, terms = -y \times y = -y^2$

STEP 9

Combine the products:
$64 + 8y - 8y - y^2$

STEP 10

Notice that $8y$ and $-8y$ are like terms and will cancel each other out:
$64 + 8y - 8y - y^2 = 64 - y^2$

STEP 11

We have simplified the expression to:
$64 - y^2$
This is the final simplified form of the product of the two binomials $(8-y)(8+y)$ .

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Multiply (8−y)(8+y)(8-y)(8+y)(8−y)(8+y) and simplify the result.

STEP 1

Assumptions1. We need to multiply the two binomials: (8−y)(8-y)(8−y) and (8+y)(8+y)(8+y).2. We will use the distributive property (also known as the FOIL method) to expand the product of these two binomials.

STEP 2

The distributive property states that for any real numbers aaa, bbb, and ccc:(a+b)(c+d)=ac+ad+bc+bd(a + b)(c + d) = ac + ad + bc + bd(a+b)(c+d)=ac+ad+bc+bdWe will apply this property to the given binomials.

STEP 3

Identify the terms in the binomials that will be multiplied together:First terms: 888 and 888. Outer terms: 888 and yyy. Inner terms: −y-y−y and 888. Last terms: −y-y−y and yyy.

STEP 4

Multiply the first terms:First terms=8×8First\, terms = 8 \times 8Firstterms=8×8

STEP 5

Multiply the outer terms:Outer terms=8×yOuter\, terms = 8 \times yOuterterms=8×y

STEP 6

Multiply the inner terms:Inner terms=−y×8Inner\, terms = -y \times 8Innerterms=−y×8

STEP 7

Multiply the last terms:Last terms=−y×yLast\, terms = -y \times yLastterms=−y×y

STEP 8

STEP 9

Combine the products:64+8y−8y−y264 + 8y - 8y - y^264+8y−8y−y2

STEP 10

Notice that 8y8y8y and −8y-8y−8y are like terms and will cancel each other out:64+8y−8y−y2=64−y264 + 8y - 8y - y^2 = 64 - y^264+8y−8y−y2=64−y2

STEP 11

We have simplified the expression to:64−y264 - y^264−y2This is the final simplified form of the product of the two binomials (8−y)(8+y)(8-y)(8+y)(8−y)(8+y).

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Multiply $(8-y)(8+y)$ and simplify the result.

Assumptions
1. We need to multiply the two binomials: $(8-y)$ and $(8+y)$ .
2. We will use the distributive property (also known as the FOIL method) to expand the product of these two binomials.

The distributive property states that for any real numbers $a$ , $b$ , and $c$ :
$(a + b)(c + d) = ac + ad + bc + bd$
We will apply this property to the given binomials.

Identify the terms in the binomials that will be multiplied together:
First terms: $8$ and $8$ . Outer terms: $8$ and $y$ . Inner terms: $-y$ and $8$ . Last terms: $-y$ and $y$ .

Multiply the first terms:
$First\, terms = 8 \times 8$

Multiply the outer terms:
$Outer\, terms = 8 \times y$

Multiply the inner terms:
$Inner\, terms = -y \times 8$

Multiply the last terms:
$Last\, terms = -y \times y$

Combine the products:
$64 + 8y - 8y - y^2$

Notice that $8y$ and $-8y$ are like terms and will cancel each other out:
$64 + 8y - 8y - y^2 = 64 - y^2$

We have simplified the expression to:
$64 - y^2$
This is the final simplified form of the product of the two binomials $(8-y)(8+y)$ .