Answer:
Part a) [tex](2m+7n)(2m-7n)[/tex]
Part b) [tex]x^2-16xy+64y^2[/tex]
Part c) [tex]216a^3b^6[/tex]
Part d) [tex](a^2-b^2)[/tex]
Step-by-step explanation:
Part a) The difference of the squares of 2m and 7n.
we know that
The difference of the squares formula is equal to
[tex](a^2-b^2)=(a+b)(a-b)[/tex]
substitute
[tex](2m)^2-(7n)^2=(2m+7n)(2m-7n)[/tex]
Part b) The square of the difference of x and 8y
The formula of the square of the difference between two numbers is equal to
[tex](a-b)^2=a^2-2ab+b^2[/tex]
substitute
[tex](x-8y)^2=x^2-2(x)(8y)+(8y)^2=x^2-16xy+64y^2[/tex]
Part c) The tripled product of 6a and b^2
we have
[tex](6ab^{2})(6ab^{2})(6ab^{2})=(6ab^{2})^3=(6^3)(a^3)(b^{2})^3=216a^3b^6[/tex]
Part d) The product of the sum of a and b and their difference
The expression is equal to
[tex](a+b)(a-b)[/tex]
The expression represent the difference of the squares between a and b
so
[tex](a+b)(a-b)=(a^2-b^2)[/tex]
The simplified expressions are:
a) 4m² - 49n²
b) x² - 16xy + 64y²
c) 18ab²
d) a² - b²
a) The difference of the squares of 2m and 7n:
(2m)² - (7n)²
= 4m² - 49n²
b) The square of the difference of x and 8y:
= (x - 8y)²
= x² - 16xy + 64y²
c) The tripled product of 6a and b²:
= 3(6a * b²)
= 3(6ab²)
= 18ab²
d) The product of the sum of a and b and their difference:
= (a + b)(a - b)
= a² - b²
The simplified expressions are:
a) 4m² - 49n²
b) x² - 16xy + 64y²
c) 18ab²
d) a² - b²
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