Mathematics, 02.11.2019 23:31 superstarsara5ouh83x

Write as an expression and simplify
a) the difference of the squares of 2m and 7n.
b)the square of the difference of x and 8y.
c)the tripled product of 6a and b^2.
d)the product of the sum of a and b and their difference.

Answers: 1

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Answer from: witcol386

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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Answer from: KaseyT

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

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

Answer from: Quest

according to this law, when unemployment goes up by 1%, gdp drops by 2%. in the question, unemployment rate goes from 2% to 5%, meaning unemployment goes up by 3%, so the gdp drops by 6%. thus the effect is a drop in gdp by 6%.

step-by-step explanation:

Answer from: Quest

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: $\sqrt{\frac{ {72x}^{16} }{ {50x}^{{{36} }}}} = \frac{ { \sqrt{72}x}^{ {16}^{ (\frac{1}{2}) } } }{ { \sqrt{50} x}^ {{36}^{ (\frac{1}{2}) } }}$ multiply exponents per exponent rules to get: $\frac{ { \sqrt{72}x}^{8} }{ { \sqrt{50}x}^{18} }$ remember you subtract exponents from the denominator and add exponents in the numerator so: $\sqrt{ \frac{72}{ 50}} \times ( {x}^{(8 - 18) } ) = \sqrt{ \frac{36}{25} } \times ( {x}^{ - 10} )$ simplify further: $\frac{6}{5} {x}^{ - 10} = \frac{6}{5 {x}^{10} }$ so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.
Plz hurrywhat is the simplified form of ? assume x ≠ 0.