(2a+3b-2c)squared?

Question

find the product

Answer 1

It is simple multiplication:
(2a + 3b - 2c)^2
=(2a + 3b - 2c)(2a + 3b - 2c)
=2a(2a + 3b - 2c) + 3b(2a + 3b - 2c) - 2c(2a + 3b - 2c)
=4a^2 + 6ab - 4ac + 6ab + 3b^2 - 6bc - 4ac + 6bc - 4c^2
=4a^2 + 12ab - 8ac + 3b^2 - 4c^2
=4a^2 + 3b^2 - 4c^2 + 12ab - 8ac

Answer 2

(2a + 3b - 2c)²
= (2a + 3b - 2c)(2a + 3b - 2c)
= 2a(2a + 3b - 2c) + 3b(2a + 3b - 2c) - 2c(2a + 3b - 2c)
= 4a² + 6ab - 4ac + 6ab + 9b² - 6bc - 4ac - 6bc + 4c²

= 4a² + 9b² + 4c² + 12ab - 8ac - 12bc

In general, any trinomial squared (excluding complex numbers) will give a six term product: each of the three terms squared plus twice each of the products of any two terms:
(x + y + z)² = x² + y² + z² + 2xy + 2xz + 2yz
A number of people answering before me incorrectly multiplied (-2c)(-2c) to get -4c² or (-2c)(+3b) to get +6bc. Be careful when distributing your negatives!

Answer 3

Nagpapatawa ba kayo?

(x + y + z) ^ 2 = x^2 + y^2 + z^2 + 2xy + 2xz + 2yz

(2a + 3b - 2c) ^ 2 = 4a^2 + 9b^2 + 4c^2 + 12ab - 8ac - 12bc

Answer 4

(2a + 3b - 2c)^2
=(2a + 3b)^2 - 2(2a+3b)(2c) + 4c^2
=4a^2 +12ab +9b^2 - 8ac - 12bc + 4c^2

Answer 5

It is a simple formula- (a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca

therefore my answer is-
(2a+3b-2c)^2
=(2a)^2+(3b)^2+(-2c)^2+2(2a*3b)+2(3b*-2c)+2(-2c*2a)
=4a^2+9b^2+4c^2+12ab-12bc-8ca

Answer 6

(2a + 3b - 2c)^2
(2a + 3b - 2c)(2a + 3b - 2c)
2a(2a + 3b - 2c) + 3b(2a + 3b - 2c) - 2c(2a + 3b - 2c)
4a^2 + 6ab - 4ac + 6ab + 3b^2 - 6bc - 4ac + 6bc - 4c^2
4a^2 + 12ab - 8ac + 3b^2 - 4c^2
4a^2 + 3b^2 - 4c^2 + 12ab - 8ac

Answer 7

combine like words. there's a 2a and -5a, so those combine to offer you a -3a: -3a + 3b + b - 7 there's a 3b and b, so those combine to offer you 4b: -3a + 4b - 7 it particularly is as simplified as you will get it.

Answer 8

~ (2a+3b-2c)^2~
(2a+3b-2c) (2a+3b-2c)
(4a^2+6ab-4ac) (6ab+9b^2-6bc) (-4ac-6bc +4c^2)
2a (a+3b-2c) + 3b (2a+3b-2c) - 2c (2a+3b-2c)
4a^2 + 6ab - 4ac + 6ab + 3b^2 - 6bc - 4ac + 6bc - 4c^2
4a^2 + 12ab - 8ac + 3b^2 - 4c^2
4a^2 + 3b^2 - 4c^2 + 12ab - 8ac

Answer 9

4a^2 + 9b^2 + 4c^2 + 12ab - 8ac - 12bc

Answer 10

you should be doing this on your own. this is the seccond time you've asked about quadratic and cubic equations. i'm very sure that your teacher is assigning you these problems for a reason. if you took the time to learn the material, you wouldn't have to ask those of us who already have.