Question

exponents and polynomials
squaring a binomial: multivariate
rewrite without parentheses and simplify.
$(9y + 21w)^2$

Explanation:

Step1: Recall the formula for squaring a binomial

The formula for squaring a binomial \((a + b)^2\) is \(a^2 + 2ab + b^2\). Here, \(a = 9y\) and \(b = 21w\).

Step2: Calculate \(a^2\)

\(a^2=(9y)^2 = 9^2\times y^2=81y^2\).

Step3: Calculate \(2ab\)

\(2ab = 2\times(9y)\times(21w)=2\times9\times21\times y\times w = 378yw\).

Step4: Calculate \(b^2\)

\(b^2=(21w)^2 = 21^2\times w^2 = 441w^2\).

Step5: Combine the terms

Adding the three terms together: \(81y^2+378yw + 441w^2\).

Answer:

\(81y^{2}+378yw + 441w^{2}\)