Solve and explain please....?

Question

25c^2+40cg+16g^2
&
v^2-10vt+25t^2

Answer 1

25c² + 40cg + 16g² = 0

The middle term is 40cg

Find the sum of the middle term

Multiply the first term 25 times the last term 16 equald 400 and factor

Factors of 400

1 x 400
2 x 200
5 x 80
8 x 50
10 x 40
20 x 20. . .←. .use these factors

+ 20 and + 20 satisfy the sum of the middkle term

insert + 20cg and + 20cg into the equation

25c² + 40cg + 16g² = 0

25c² + 20cg + 20cg + 16g² = 0

Group factor

(25c² + 20cg) + (20cg + 16g²) = 0

5c(5c + 4g) + 4g(5c + 4g) = 0

(5c + 4g)(5c + 4g) = 0

- - - - - - - -s-

Answer 2

Facor each expression by grouping:

Find the product of the first and last term:
(25c^2)(16g^2) = 400(c^2)(g^2)

Find a pair of factors of 400(c^2)(g^2) that have a sum of the middle term 40cg:
(20cg)(20cg) = 400(c^2)(g^2)
and
20cg + 20cg = 40cg

Replace the middle term with the sum of the pair of factors, and factor two terms at a time:

25c^2 + 20cg + 20cg + 16g^2
= 5c(5c + 4g) + 4g(5c + 4g)
= (5c + 4g)(5c + 4g)


v^2 - 10 vt + 25t^2
= v^2 - 5vt - 5vt + 25t^2
= v(v - 5t) - 5t(v - 5t)
= (v - 5t)(v - 5t)

Answer 3

this is simple factoring.
(5c + 4g) (5c + 4g)
multiply the factors and you get:
5c x 5c = 25c^2

4g x 4g = 16g^2
4g x 5c = 20 cg
5c x 4g = 20 cg
add and you get 25c^2 + 40cg + 16g^2

(v - 5t) (v - 5t)
multiply the factors:
v x v = v^2
5t x 5t = 25t^2
-5t x v = -5vt
v x -5t = -5vt
add and you get v^2 -10vt +25t^2

Answer 4

(5c + 4g)^2 : A perfect square trinomial.
Get these by : Root first term, root last term, check if twice product of these is middle term. 5 x 4 x 2 is 40 so this one is.

(v - 5t)^2 : a perfect square trinomial also.
1 x - 5 x 2 = -10, so this works as well.

Answer 5

(5c + 4g)(5c + 4g)

5c * 5c = 25c²
4g * 4g = 16g²
2 * (5c * 4g) = 2 * (20cg) = 40cg

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(v - 5t)(v - 5t)

v * v = v²
(-5t) * (-5t) = 25t²
2 * (v * (-5t)) = 2 * (-5vt) = -10vt