Math / Algebra

QuestionMultiply and add like terms: $(4 w+5)(4 w-5)$

Studdy Solution

STEP 1

1. We are asked to multiply two binomials.
2. The expression is in the form of a difference of squares.
3. We will use the formula for the difference of squares to simplify the multiplication.

STEP 2

1. Recognize the form of the expression as a difference of squares.
2. Apply the difference of squares formula.
3. Simplify the resulting expression.

STEP 3

Recognize that the expression $(4w + 5)(4w - 5)$ is in the form of a difference of squares, which is given by:
$(a + b)(a - b) = a^2 - b^2$
Here, $a = 4w$ and $b = 5$ .

STEP 4

Apply the difference of squares formula:
$(4w + 5)(4w - 5) = (4w)^2 - 5^2$

STEP 5

Simplify the expression:
Calculate $(4w)^2$ :
$(4w)^2 = 16w^2$
Calculate $5^2$ :
$5^2 = 25$
Substitute back into the expression:
$16w^2 - 25$
The simplified expression is:
$\boxed{16w^2 - 25}$

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QuestionMultiply and add like terms: $(4 w+5)(4 w-5)$

Studdy Solution

STEP 1

1. We are asked to multiply two binomials.
2. The expression is in the form of a difference of squares.
3. We will use the formula for the difference of squares to simplify the multiplication.

STEP 2

1. Recognize the form of the expression as a difference of squares.
2. Apply the difference of squares formula.
3. Simplify the resulting expression.

STEP 3

Recognize that the expression $(4w + 5)(4w - 5)$ is in the form of a difference of squares, which is given by:
$(a + b)(a - b) = a^2 - b^2$
Here, $a = 4w$ and $b = 5$ .

STEP 4

Apply the difference of squares formula:
$(4w + 5)(4w - 5) = (4w)^2 - 5^2$

STEP 5

Simplify the expression:
Calculate $(4w)^2$ :
$(4w)^2 = 16w^2$
Calculate $5^2$ :
$5^2 = 25$
Substitute back into the expression:
$16w^2 - 25$
The simplified expression is:
$\boxed{16w^2 - 25}$

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QuestionMultiply and add like terms: (4w+5)(4w−5)(4 w+5)(4 w-5)(4w+5)(4w−5)

Studdy Solution

STEP 1

1. We are asked to multiply two binomials.2. The expression is in the form of a difference of squares.3. We will use the formula for the difference of squares to simplify the multiplication.

STEP 2

1. Recognize the form of the expression as a difference of squares.2. Apply the difference of squares formula.3. Simplify the resulting expression.

STEP 3

Recognize that the expression (4w+5)(4w−5)(4w + 5)(4w - 5)(4w+5)(4w−5) is in the form of a difference of squares, which is given by:(a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2(a+b)(a−b)=a2−b2Here, a=4wa = 4wa=4w and b=5b = 5b=5.

STEP 4

Apply the difference of squares formula:(4w+5)(4w−5)=(4w)2−52(4w + 5)(4w - 5) = (4w)^2 - 5^2(4w+5)(4w−5)=(4w)2−52

STEP 5

Simplify the expression:Calculate (4w)2(4w)^2(4w)2:(4w)2=16w2(4w)^2 = 16w^2(4w)2=16w2Calculate 525^252:52=255^2 = 2552=25Substitute back into the expression:16w2−2516w^2 - 2516w2−25The simplified expression is:16w2−25 \boxed{16w^2 - 25} 16w2−25​

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QuestionMultiply and add like terms: $(4 w+5)(4 w-5)$

1. We are asked to multiply two binomials.
2. The expression is in the form of a difference of squares.
3. We will use the formula for the difference of squares to simplify the multiplication.

1. Recognize the form of the expression as a difference of squares.
2. Apply the difference of squares formula.
3. Simplify the resulting expression.

Recognize that the expression $(4w + 5)(4w - 5)$ is in the form of a difference of squares, which is given by:
$(a + b)(a - b) = a^2 - b^2$
Here, $a = 4w$ and $b = 5$ .

Apply the difference of squares formula:
$(4w + 5)(4w - 5) = (4w)^2 - 5^2$

Simplify the expression:
Calculate $(4w)^2$ :
$(4w)^2 = 16w^2$
Calculate $5^2$ :
$5^2 = 25$
Substitute back into the expression:
$16w^2 - 25$
The simplified expression is:
$\boxed{16w^2 - 25}$