Solved on Feb 12, 2024

Expand the expression $(2x+6)(2x+5)$ and express the result as a trinomial.

STEP 1

Assumptions
1. We are given a binomial expression $(2x + 6)$ .
2. We are given another binomial expression $(2x + 5)$ .
3. We need to multiply these binomials to get a trinomial.

STEP 2

To multiply two binomials, we use the distributive property (also known as the FOIL method, which stands for First, Outer, Inner, Last) to expand the product.
$(a + b)(c + d) = ac + ad + bc + bd$

STEP 3

Identify the components of each binomial that will be multiplied together.
First terms: $2x$ and $2x$
Outer terms: $2x$ and $5$
Inner terms: $6$ and $2x$
Last terms: $6$ and $5$

STEP 4

Multiply the first terms from each binomial.
$First = 2x \cdot 2x = 4x^2$

STEP 5

Multiply the outer terms from each binomial.
$Outer = 2x \cdot 5 = 10x$

STEP 6

Multiply the inner terms from each binomial.
$Inner = 6 \cdot 2x = 12x$

STEP 7

Multiply the last terms from each binomial.
$Last = 6 \cdot 5 = 30$

STEP 8

Combine the results from steps 4, 5, 6, and 7 to form the expanded expression.
$4x^2 + 10x + 12x + 30$

STEP 9

Combine like terms in the expanded expression.
$4x^2 + (10x + 12x) + 30$

STEP 10

Add the like terms (the terms with $x$ ).
$4x^2 + 22x + 30$

STEP 11

The expression $4x^2 + 22x + 30$ is the trinomial form of the product of the given binomials.
Expressed as a trinomial, $(2x + 6)(2x + 5) = 4x^2 + 22x + 30$ .

Was this helpful?

Expand the expression $(2x+6)(2x+5)$ and express the result as a trinomial.

STEP 1

Assumptions
1. We are given a binomial expression $(2x + 6)$ .
2. We are given another binomial expression $(2x + 5)$ .
3. We need to multiply these binomials to get a trinomial.

STEP 2

To multiply two binomials, we use the distributive property (also known as the FOIL method, which stands for First, Outer, Inner, Last) to expand the product.
$(a + b)(c + d) = ac + ad + bc + bd$

STEP 3

Identify the components of each binomial that will be multiplied together.
First terms: $2x$ and $2x$
Outer terms: $2x$ and $5$
Inner terms: $6$ and $2x$
Last terms: $6$ and $5$

STEP 4

Multiply the first terms from each binomial.
$First = 2x \cdot 2x = 4x^2$

STEP 5

Multiply the outer terms from each binomial.
$Outer = 2x \cdot 5 = 10x$

STEP 6

Multiply the inner terms from each binomial.
$Inner = 6 \cdot 2x = 12x$

STEP 7

Multiply the last terms from each binomial.
$Last = 6 \cdot 5 = 30$

STEP 8

Combine the results from steps 4, 5, 6, and 7 to form the expanded expression.
$4x^2 + 10x + 12x + 30$

STEP 9

Combine like terms in the expanded expression.
$4x^2 + (10x + 12x) + 30$

STEP 10

Add the like terms (the terms with $x$ ).
$4x^2 + 22x + 30$

STEP 11

The expression $4x^2 + 22x + 30$ is the trinomial form of the product of the given binomials.
Expressed as a trinomial, $(2x + 6)(2x + 5) = 4x^2 + 22x + 30$ .

Start learning now

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

Expand the expression (2x+6)(2x+5)(2x+6)(2x+5)(2x+6)(2x+5) and express the result as a trinomial.

STEP 1

Assumptions1. We are given a binomial expression (2x+6)(2x + 6)(2x+6).2. We are given another binomial expression (2x+5)(2x + 5)(2x+5).3. We need to multiply these binomials to get a trinomial.

STEP 2

To multiply two binomials, we use the distributive property (also known as the FOIL method, which stands for First, Outer, Inner, Last) to expand the product.(a+b)(c+d)=ac+ad+bc+bd(a + b)(c + d) = ac + ad + bc + bd(a+b)(c+d)=ac+ad+bc+bd

STEP 3

Identify the components of each binomial that will be multiplied together.First terms: 2x2x2x and 2x2x2xOuter terms: 2x2x2x and 555Inner terms: 666 and 2x2x2xLast terms: 666 and 555

STEP 4

Multiply the first terms from each binomial.First=2x⋅2x=4x2First = 2x \cdot 2x = 4x^2First=2x⋅2x=4x2

STEP 5

Multiply the outer terms from each binomial.Outer=2x⋅5=10xOuter = 2x \cdot 5 = 10xOuter=2x⋅5=10x

STEP 6

Multiply the inner terms from each binomial.Inner=6⋅2x=12xInner = 6 \cdot 2x = 12xInner=6⋅2x=12x

STEP 7

Multiply the last terms from each binomial.Last=6⋅5=30Last = 6 \cdot 5 = 30Last=6⋅5=30

STEP 8

Combine the results from steps 4, 5, 6, and 7 to form the expanded expression.4x2+10x+12x+304x^2 + 10x + 12x + 304x2+10x+12x+30

STEP 9

Combine like terms in the expanded expression.4x2+(10x+12x)+304x^2 + (10x + 12x) + 304x2+(10x+12x)+30

STEP 10

Add the like terms (the terms with xxx).4x2+22x+304x^2 + 22x + 304x2+22x+30

STEP 11

The expression 4x2+22x+304x^2 + 22x + 304x2+22x+30 is the trinomial form of the product of the given binomials.Expressed as a trinomial, (2x+6)(2x+5)=4x2+22x+30(2x + 6)(2x + 5) = 4x^2 + 22x + 30(2x+6)(2x+5)=4x2+22x+30.

Start learning now

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

Expand the expression $(2x+6)(2x+5)$ and express the result as a trinomial.

Assumptions
1. We are given a binomial expression $(2x + 6)$ .
2. We are given another binomial expression $(2x + 5)$ .
3. We need to multiply these binomials to get a trinomial.

To multiply two binomials, we use the distributive property (also known as the FOIL method, which stands for First, Outer, Inner, Last) to expand the product.
$(a + b)(c + d) = ac + ad + bc + bd$

Identify the components of each binomial that will be multiplied together.
First terms: $2x$ and $2x$
Outer terms: $2x$ and $5$
Inner terms: $6$ and $2x$
Last terms: $6$ and $5$

Multiply the first terms from each binomial.
$First = 2x \cdot 2x = 4x^2$

Multiply the outer terms from each binomial.
$Outer = 2x \cdot 5 = 10x$

Multiply the inner terms from each binomial.
$Inner = 6 \cdot 2x = 12x$

Multiply the last terms from each binomial.
$Last = 6 \cdot 5 = 30$

Combine the results from steps 4, 5, 6, and 7 to form the expanded expression.
$4x^2 + 10x + 12x + 30$

Combine like terms in the expanded expression.
$4x^2 + (10x + 12x) + 30$

Add the like terms (the terms with $x$ ).
$4x^2 + 22x + 30$

The expression $4x^2 + 22x + 30$ is the trinomial form of the product of the given binomials.
Expressed as a trinomial, $(2x + 6)(2x + 5) = 4x^2 + 22x + 30$ .