Question

Find the product [(5q+6)-p][(5q+6)+p]

Answer 1

Hello there!


Math by itself isn't an easy subject. When they give us to solve something, teachers often makes it tricky for us. Just like in this case.

Let's get started!

[(5q + 6)-p][(5q + 6)+p]

Just eliminate [ , they are just here to make it seems scary :)

(5q + 6 - p)(5q + 6 + p)

Use the distributive form

(5q)(5q) + (5q)(6) + (5q)(q) + (6)(5q) + (6)(6) + (6)(p) + (-q)(5q) + (-q)(6) + (-q)(p)

= 25x² + 30q + 5pq + 30q + 36 + 6 - 5pq - 6p -p²

=-p² + 25q² + 60q + 36

P.S. Sorry for the late answer, my pc restarted by itself. It is getting old :)

Answer 2

Let x = 5q+6

[(5q+6)-p][(5q+6)+p] will turn into (x-p)(x+p) based on that substitution

Use the difference of squares rule
(x-p)(x+p) = x^2 - p^2

Then determine what x^2 is equal to in terms of q
x = 5q+6
x^2 = (5q+6)^2
x^2 = (5q+6)(5q+6)
x^2 = 5q(5q+6)+6(5q+6)
x^2 = 25q^2+30q+30q+36
x^2 = 25q^2+60q+36

So
x^2 - p^2
updates to
25q^2+60q+36-p^2

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The final answer is 25q^2+60q+36-p^2