Question

i) Which expression is a factor of m^2 -16?
ii)a^2 - 2ab + b^2 is the same as
iii)The product of (2x+7) and (2x–7) is
iv)If x=2, then the value of 4x^2+ 12x + 9 is

Answer 1

Answer:

(i) Factors of m² - 16 are (m + 4) and (m - 4)

(ii) (a + b)²

(iii) 4x² - 49

(iv) 49

Step-by-step explanation:

(i)

We know that,

a² - b² = (a + b)(a - b)

Now, back to the Question,

m² - 16

= (m)² - (4)²

= (m + 4)(m - 4)

Thus, (m + 4) and (m - 4) are the factors of the expression m² - 16

(ii)

We know that,

(x - y)² = x² - 2xy + y²

Now, back to the Question,

a² - 2ab + b² will be equal to (a + b)²

Thus,

a² - 2ab + b² = (a + b)²

(iii)

We know that,

(a + b)(a - b) = a² - b²

Now, back to the Question,

(2x + 7)(2x - 7)

= (2x)² - 7²

= (2²x²) - 49

= 4x² - 49

(iv)

Let p(x) = 4x² + 12x + 9

x = 2

p(2) = 4(2)² + 12(2) + 9

p(2) = 4(4) + 24 + 9

p(2) = 16 + 24 + 9

p(2) = 49

Thus, p(x) = 49 when x = 2

Hope it helped and you understood it........All the best