Question

Write as an expression and simplify

Answer 1

Answer:

Part a) $(2m+7n)(2m-7n)$

Part b) $x^2-16xy+64y^2$

Part c) $216a^3b^6$

Part d)  $(a^2-b^2)$

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

$(a^2-b^2)=(a+b)(a-b)$

substitute

$(2m)^2-(7n)^2=(2m+7n)(2m-7n)$

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

$(a-b)^2=a^2-2ab+b^2$

substitute

$(x-8y)^2=x^2-2(x)(8y)+(8y)^2=x^2-16xy+64y^2$

Part c) The tripled product of 6a and b^2

we have

$(6ab^{2})(6ab^{2})(6ab^{2})=(6ab^{2})^3=(6^3)(a^3)(b^{2})^3=216a^3b^6$

Part d) The product of the sum of a and b and their difference

The expression is equal to

$(a+b)(a-b)$

The expression represent the difference of the squares between a and b

so

$(a+b)(a-b)=(a^2-b^2)$