Answer:
The product of [tex]\left(2x+\:5y\right)\left(2x\:−\:5y\right)[/tex] is
[tex]4x^2-25y^2[/tex]
Step-by-step explanation:
Given : (2x+ 5y) and (2x−5y).
We have to find the product of [tex]\left(2x+\:5y\right)\left(2x\:−\:5y\right)[/tex]
Consider , the given expression [tex]\left(2x+\:5y\right)\left(2x\:−\:5y\right)[/tex]
Applying the difference of two square formula,
[tex]\left(a+b\right)\left(a-b\right)=a^2-b^2[/tex]
We have,
[tex]=\left(2x\right)^2-\left(5y\right)^2[/tex]
Apply exponent rule, [tex]\left(a\cdot \:b\right)^n=a^nb^n[/tex]
[tex]=2^2x^2-5^2y^2[/tex]
Simplify, we have,
[tex]=4x^2-25y^2[/tex]
Thus, the product of [tex]\left(2x+\:5y\right)\left(2x\:−\:5y\right)[/tex] is
[tex]4x^2-25y^2[/tex]
