Solved on Jan 24, 2024

Multiply the polynomials $(4x+1)$ and $(-3x+5)$ .

STEP 1

Assumptions
1. We are multiplying two binomials: $(4x + 1)$ and $(-3x + 5)$ .
2. To multiply the binomials, we will use the distributive property (also known as the FOIL method, which stands for First, Outer, Inner, Last).

STEP 2

First, we multiply the first terms from each binomial.
$First = 4x \cdot (-3x)$

STEP 3

Calculate the product of the first terms.
$First = -12x^2$

STEP 4

Next, we multiply the outer terms from each binomial.
$Outer = 4x \cdot 5$

STEP 5

Calculate the product of the outer terms.
$Outer = 20x$

STEP 6

Now, we multiply the inner terms from each binomial.
$Inner = 1 \cdot (-3x)$

STEP 7

Calculate the product of the inner terms.
$Inner = -3x$

STEP 8

Finally, we multiply the last terms from each binomial.
$Last = 1 \cdot 5$

STEP 9

Calculate the product of the last terms.
$Last = 5$

STEP 10

Combine the products from the First, Outer, Inner, and Last steps to get the expanded form of the polynomial.
$Expanded\, form = First + Outer + Inner + Last$

STEP 11

Substitute the calculated products into the expanded form.
$Expanded\, form = -12x^2 + 20x - 3x + 5$

STEP 12

Combine like terms to simplify the expression.
$Simplified\, form = -12x^2 + (20x - 3x) + 5$

STEP 13

Finish combining like terms.
$Simplified\, form = -12x^2 + 17x + 5$
The product of the polynomials $(4x + 1)(-3x + 5)$ is $-12x^2 + 17x + 5$ .

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Multiply the polynomials $(4x+1)$ and $(-3x+5)$ .

STEP 1

Assumptions
1. We are multiplying two binomials: $(4x + 1)$ and $(-3x + 5)$ .
2. To multiply the binomials, we will use the distributive property (also known as the FOIL method, which stands for First, Outer, Inner, Last).

STEP 2

First, we multiply the first terms from each binomial.
$First = 4x \cdot (-3x)$

STEP 3

Calculate the product of the first terms.
$First = -12x^2$

STEP 4

Next, we multiply the outer terms from each binomial.
$Outer = 4x \cdot 5$

STEP 5

Calculate the product of the outer terms.
$Outer = 20x$

STEP 6

Now, we multiply the inner terms from each binomial.
$Inner = 1 \cdot (-3x)$

STEP 7

Calculate the product of the inner terms.
$Inner = -3x$

STEP 8

Finally, we multiply the last terms from each binomial.
$Last = 1 \cdot 5$

STEP 9

Calculate the product of the last terms.
$Last = 5$

STEP 10

Combine the products from the First, Outer, Inner, and Last steps to get the expanded form of the polynomial.
$Expanded\, form = First + Outer + Inner + Last$

STEP 11

Substitute the calculated products into the expanded form.
$Expanded\, form = -12x^2 + 20x - 3x + 5$

STEP 12

Combine like terms to simplify the expression.
$Simplified\, form = -12x^2 + (20x - 3x) + 5$

STEP 13

Finish combining like terms.
$Simplified\, form = -12x^2 + 17x + 5$
The product of the polynomials $(4x + 1)(-3x + 5)$ is $-12x^2 + 17x + 5$ .

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Multiply the polynomials (4x+1)(4x+1)(4x+1) and (−3x+5)(-3x+5)(−3x+5).

STEP 1

Assumptions1. We are multiplying two binomials: (4x+1)(4x + 1)(4x+1) and (−3x+5)(-3x + 5)(−3x+5).2. To multiply the binomials, we will use the distributive property (also known as the FOIL method, which stands for First, Outer, Inner, Last).

STEP 2

First, we multiply the first terms from each binomial.First=4x⋅(−3x)First = 4x \cdot (-3x)First=4x⋅(−3x)

STEP 3

Calculate the product of the first terms.First=−12x2First = -12x^2First=−12x2

STEP 4

Next, we multiply the outer terms from each binomial.Outer=4x⋅5Outer = 4x \cdot 5Outer=4x⋅5

STEP 5

Calculate the product of the outer terms.Outer=20xOuter = 20xOuter=20x

STEP 6

Now, we multiply the inner terms from each binomial.Inner=1⋅(−3x)Inner = 1 \cdot (-3x)Inner=1⋅(−3x)

STEP 7

Calculate the product of the inner terms.Inner=−3xInner = -3xInner=−3x

STEP 8

Finally, we multiply the last terms from each binomial.Last=1⋅5Last = 1 \cdot 5Last=1⋅5

STEP 9

Calculate the product of the last terms.Last=5Last = 5Last=5

STEP 10

Combine the products from the First, Outer, Inner, and Last steps to get the expanded form of the polynomial.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=−12x2+20x−3x+5Expanded\, form = -12x^2 + 20x - 3x + 5Expandedform=−12x2+20x−3x+5

STEP 12

Combine like terms to simplify the expression.Simplified form=−12x2+(20x−3x)+5Simplified\, form = -12x^2 + (20x - 3x) + 5Simplifiedform=−12x2+(20x−3x)+5

STEP 13

Finish combining like terms.Simplified form=−12x2+17x+5Simplified\, form = -12x^2 + 17x + 5Simplifiedform=−12x2+17x+5The product of the polynomials (4x+1)(−3x+5)(4x + 1)(-3x + 5)(4x+1)(−3x+5) is −12x2+17x+5-12x^2 + 17x + 5−12x2+17x+5.

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Multiply the polynomials $(4x+1)$ and $(-3x+5)$ .

Assumptions
1. We are multiplying two binomials: $(4x + 1)$ and $(-3x + 5)$ .
2. To multiply the binomials, we will use the distributive property (also known as the FOIL method, which stands for First, Outer, Inner, Last).

First, we multiply the first terms from each binomial.
$First = 4x \cdot (-3x)$

Calculate the product of the first terms.
$First = -12x^2$

Next, we multiply the outer terms from each binomial.
$Outer = 4x \cdot 5$

Calculate the product of the outer terms.
$Outer = 20x$

Now, we multiply the inner terms from each binomial.
$Inner = 1 \cdot (-3x)$

Calculate the product of the inner terms.
$Inner = -3x$

Finally, we multiply the last terms from each binomial.
$Last = 1 \cdot 5$

Calculate the product of the last terms.
$Last = 5$

Combine the products from the First, Outer, Inner, and Last steps to get the expanded form of the polynomial.
$Expanded\, form = First + Outer + Inner + Last$

Substitute the calculated products into the expanded form.
$Expanded\, form = -12x^2 + 20x - 3x + 5$

Combine like terms to simplify the expression.
$Simplified\, form = -12x^2 + (20x - 3x) + 5$

Finish combining like terms.
$Simplified\, form = -12x^2 + 17x + 5$
The product of the polynomials $(4x + 1)(-3x + 5)$ is $-12x^2 + 17x + 5$ .