# Multiply the polynomials using the special product formulas. Express your

Ben Shaver 2021-12-16 Answered
Multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form.
${\left(x-2y\right)}^{2}$
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## Expert Answer

Dabanka4v
Answered 2021-12-17 Author has 36 answers
Step 1
Given:
${\left(x-2y\right)}^{2}$
To multiply the polynomial express in standard form
Step 2
Special Identity ${\left(a-b\right)}^{2}={a}^{2}-2ab+{b}^{2}$
a=x; b=2y
${\left(x-2y\right)}^{2}={\left(x\right)}^{2}-2\left(x\right)\left(2y\right)+{\left(2y\right)}^{2}$
$={x}^{2}-4xy+4{y}^{2}$
Answer: ${x}^{2}-4xy+4{y}^{2}$
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Barbara Meeker
Answered 2021-12-18 Author has 38 answers
The given expression is the square of a binomial. So, multiply the binomials using the special products formula ${\left(x-a\right)}^{2}={x}^{2}-2ax+{a}^{2}$.
${\left(x-2y\right)}^{2}={x}^{2}-2\cdot 2y\cdot x+{\left(2y\right)}^{2}$
Rewrite using the laws of exponents and simplify.
${x}^{2}-2\cdot 2y\cdot x+{\left(2y\right)}^{2}={x}^{2}-4xy+{2}^{2}{y}^{2}$
$={x}^{2}-4xy+4{y}^{2}$
Therefore, the result is ${x}^{2}-4xy+4{y}^{2}$.
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