Solved on Dec 12, 2023

Multiply and simplify $(4x+2)(4x+5)$

STEP 1

Assumptions
1. We are given the expression $(4x + 2)(4x + 5)$ .
2. We will use the distributive property (also known as the FOIL method for binomials) to multiply the two binomials.
3. Simplify the resulting expression by combining like terms.

STEP 2

Apply the distributive property (FOIL method) to multiply the two binomials. FOIL stands for First, Outer, Inner, Last, which represents the order in which we multiply the terms of the binomials.
$(4x + 2)(4x + 5) = (4x \cdot 4x) + (4x \cdot 5) + (2 \cdot 4x) + (2 \cdot 5)$

STEP 3

Multiply the first terms of each binomial (First).
$4x \cdot 4x = 16x^2$

STEP 4

Multiply the outer terms of the binomials (Outer).
$4x \cdot 5 = 20x$

STEP 5

Multiply the inner terms of the binomials (Inner).
$2 \cdot 4x = 8x$

STEP 6

Multiply the last terms of each binomial (Last).
$2 \cdot 5 = 10$

STEP 7

Combine the results from steps 3, 4, 5, and 6.
$(4x + 2)(4x + 5) = 16x^2 + 20x + 8x + 10$

STEP 8

Combine the like terms, which are the terms with the same variable and exponent. In this case, $20x$ and $8x$ are like terms.
$16x^2 + 20x + 8x + 10 = 16x^2 + (20x + 8x) + 10$

STEP 9

Add the like terms.
$16x^2 + (20x + 8x) + 10 = 16x^2 + 28x + 10$

STEP 10

The expression is now simplified completely.
$(4x + 2)(4x + 5) = 16x^2 + 28x + 10$
The simplified result of multiplying and simplifying the expression $(4x + 2)(4x + 5)$ is $16x^2 + 28x + 10$ .

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Multiply and simplify $(4x+2)(4x+5)$

STEP 1

Assumptions
1. We are given the expression $(4x + 2)(4x + 5)$ .
2. We will use the distributive property (also known as the FOIL method for binomials) to multiply the two binomials.
3. Simplify the resulting expression by combining like terms.

STEP 2

Apply the distributive property (FOIL method) to multiply the two binomials. FOIL stands for First, Outer, Inner, Last, which represents the order in which we multiply the terms of the binomials.
$(4x + 2)(4x + 5) = (4x \cdot 4x) + (4x \cdot 5) + (2 \cdot 4x) + (2 \cdot 5)$

STEP 3

Multiply the first terms of each binomial (First).
$4x \cdot 4x = 16x^2$

STEP 4

Multiply the outer terms of the binomials (Outer).
$4x \cdot 5 = 20x$

STEP 5

Multiply the inner terms of the binomials (Inner).
$2 \cdot 4x = 8x$

STEP 6

Multiply the last terms of each binomial (Last).
$2 \cdot 5 = 10$

STEP 7

Combine the results from steps 3, 4, 5, and 6.
$(4x + 2)(4x + 5) = 16x^2 + 20x + 8x + 10$

STEP 8

Combine the like terms, which are the terms with the same variable and exponent. In this case, $20x$ and $8x$ are like terms.
$16x^2 + 20x + 8x + 10 = 16x^2 + (20x + 8x) + 10$

STEP 9

Add the like terms.
$16x^2 + (20x + 8x) + 10 = 16x^2 + 28x + 10$

STEP 10

The expression is now simplified completely.
$(4x + 2)(4x + 5) = 16x^2 + 28x + 10$
The simplified result of multiplying and simplifying the expression $(4x + 2)(4x + 5)$ is $16x^2 + 28x + 10$ .

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Multiply and simplify (4x+2)(4x+5)(4x+2)(4x+5)(4x+2)(4x+5)

STEP 1

Assumptions1. We are given the expression (4x+2)(4x+5)(4x + 2)(4x + 5)(4x+2)(4x+5).2. We will use the distributive property (also known as the FOIL method for binomials) to multiply the two binomials.3. Simplify the resulting expression by combining like terms.

STEP 2

STEP 3

Multiply the first terms of each binomial (First).4x⋅4x=16x2 4x \cdot 4x = 16x^2 4x⋅4x=16x2

STEP 4

Multiply the outer terms of the binomials (Outer).4x⋅5=20x 4x \cdot 5 = 20x 4x⋅5=20x

STEP 5

Multiply the inner terms of the binomials (Inner).2⋅4x=8x 2 \cdot 4x = 8x 2⋅4x=8x

STEP 6

Multiply the last terms of each binomial (Last).2⋅5=10 2 \cdot 5 = 10 2⋅5=10

STEP 7

Combine the results from steps 3, 4, 5, and 6.(4x+2)(4x+5)=16x2+20x+8x+10 (4x + 2)(4x + 5) = 16x^2 + 20x + 8x + 10 (4x+2)(4x+5)=16x2+20x+8x+10

STEP 8

Combine the like terms, which are the terms with the same variable and exponent. In this case, 20x20x20x and 8x8x8x are like terms.16x2+20x+8x+10=16x2+(20x+8x)+10 16x^2 + 20x + 8x + 10 = 16x^2 + (20x + 8x) + 10 16x2+20x+8x+10=16x2+(20x+8x)+10

STEP 9

Add the like terms.16x2+(20x+8x)+10=16x2+28x+10 16x^2 + (20x + 8x) + 10 = 16x^2 + 28x + 10 16x2+(20x+8x)+10=16x2+28x+10

STEP 10

The expression is now simplified completely.(4x+2)(4x+5)=16x2+28x+10 (4x + 2)(4x + 5) = 16x^2 + 28x + 10 (4x+2)(4x+5)=16x2+28x+10The simplified result of multiplying and simplifying the expression (4x+2)(4x+5)(4x + 2)(4x + 5)(4x+2)(4x+5) is 16x2+28x+1016x^2 + 28x + 1016x2+28x+10.

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Multiply and simplify $(4x+2)(4x+5)$

Assumptions
1. We are given the expression $(4x + 2)(4x + 5)$ .
2. We will use the distributive property (also known as the FOIL method for binomials) to multiply the two binomials.
3. Simplify the resulting expression by combining like terms.

Multiply the first terms of each binomial (First).
$4x \cdot 4x = 16x^2$

Multiply the outer terms of the binomials (Outer).
$4x \cdot 5 = 20x$

Multiply the inner terms of the binomials (Inner).
$2 \cdot 4x = 8x$

Multiply the last terms of each binomial (Last).
$2 \cdot 5 = 10$

Combine the results from steps 3, 4, 5, and 6.
$(4x + 2)(4x + 5) = 16x^2 + 20x + 8x + 10$

Combine the like terms, which are the terms with the same variable and exponent. In this case, $20x$ and $8x$ are like terms.
$16x^2 + 20x + 8x + 10 = 16x^2 + (20x + 8x) + 10$

Add the like terms.
$16x^2 + (20x + 8x) + 10 = 16x^2 + 28x + 10$

The expression is now simplified completely.
$(4x + 2)(4x + 5) = 16x^2 + 28x + 10$
The simplified result of multiplying and simplifying the expression $(4x + 2)(4x + 5)$ is $16x^2 + 28x + 10$ .