Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Oct 23, 2023

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

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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