Question Simplify the expression $(4 x-5 y)^{2}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression (4x -5y)^.

STEP 2

The expression $(4x -5y)^2$ is a squared binomial. The square of a binomial $(a - b)^2$ can be expanded using the formula $(a - b)^2 = a^2 -2ab + b^2$ .

STEP 3

Now, we can apply this formula to our expression $(x -5y)^2$ . Here, $a =x$ and $b =5y$ .

STEP 4

Substitute $a =4x$ and $b =y$ into the formula.
$(4x -y)^2 = (4x)^2 -2(4x)(y) + (y)^2$

STEP 5

implify the expression by performing the operations.
$(4x -5y)^2 =16x^2 -40xy +25y^2$ So, the simplified form of $(4x -5y)^2$ is $16x^2 -40xy +25y^2$ .

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Question Simplify the expression $(4 x-5 y)^{2}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression (4x -5y)^.

STEP 2

The expression $(4x -5y)^2$ is a squared binomial. The square of a binomial $(a - b)^2$ can be expanded using the formula $(a - b)^2 = a^2 -2ab + b^2$ .

STEP 3

Now, we can apply this formula to our expression $(x -5y)^2$ . Here, $a =x$ and $b =5y$ .

STEP 4

Substitute $a =4x$ and $b =y$ into the formula.
$(4x -y)^2 = (4x)^2 -2(4x)(y) + (y)^2$

STEP 5

implify the expression by performing the operations.
$(4x -5y)^2 =16x^2 -40xy +25y^2$ So, the simplified form of $(4x -5y)^2$ is $16x^2 -40xy +25y^2$ .

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Question Simplify the expression (4x−5y)2(4 x-5 y)^{2}(4x−5y)2.

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression (4x -5y)^.

STEP 2

The expression (4x−5y)2(4x -5y)^2(4x−5y)2 is a squared binomial. The square of a binomial (a−b)2(a - b)^2(a−b)2 can be expanded using the formula (a−b)2=a2−2ab+b2(a - b)^2 = a^2 -2ab + b^2(a−b)2=a2−2ab+b2.

STEP 3

Now, we can apply this formula to our expression (x−5y)2(x -5y)^2(x−5y)2. Here, a=xa =xa=x and b=5yb =5yb=5y.

STEP 4

Substitute a=4xa =4xa=4x and b=yb =yb=y into the formula.(4x−y)2=(4x)2−2(4x)(y)+(y)2(4x -y)^2 = (4x)^2 -2(4x)(y) + (y)^2(4x−y)2=(4x)2−2(4x)(y)+(y)2

STEP 5

implify the expression by performing the operations.(4x−5y)2=16x2−40xy+25y2(4x -5y)^2 =16x^2 -40xy +25y^2(4x−5y)2=16x2−40xy+25y2So, the simplified form of (4x−5y)2(4x -5y)^2(4x−5y)2 is 16x2−40xy+25y216x^2 -40xy +25y^216x2−40xy+25y2.

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Question Simplify the expression $(4 x-5 y)^{2}$ .

The expression $(4x -5y)^2$ is a squared binomial. The square of a binomial $(a - b)^2$ can be expanded using the formula $(a - b)^2 = a^2 -2ab + b^2$ .

Now, we can apply this formula to our expression $(x -5y)^2$ . Here, $a =x$ and $b =5y$ .

Substitute $a =4x$ and $b =y$ into the formula.
$(4x -y)^2 = (4x)^2 -2(4x)(y) + (y)^2$

implify the expression by performing the operations.
$(4x -5y)^2 =16x^2 -40xy +25y^2$ So, the simplified form of $(4x -5y)^2$ is $16x^2 -40xy +25y^2$ .