20 Examples of Square Binomial

The binomials are mathematical expressions in which two members or terms appear, either numbers or abstract representations that generalize a finite or infinite quantity of numbers. The binomials they are, therefore, compositions of two terms.

In mathematical language, it is understood by finished the operational unit that is separated from another by an addition (+) or subtraction (-) sign. Combinations of expressions separated by other mathematical operators do not fall into this category.

The square binomials (or binomials squared) are those in which the addition or subtraction of two terms must be raised to the power two. An important fact about empowerment is that the sum of two squared numbers is not equal to the sum of the squares of those two numbers, but must also be added one more term that includes twice the product of A and B. For example:(X + 1)² = X² + 2X + 1, (3 + 6)² = 81, (56-36)² = 400.

This is precisely what motivated Newton already Pascal to elaborate two considerations that are very useful when it comes to understanding the dynamics of these powers: Newton's theorem and Pascal's triangles:

The Newton's theorem, which like every mathematical theorem has a proof, shows that the expansion of (A + B)^N has N + 1 terms, of which the powers of A start with N as an exponent in the first and decrease to 0 in the last, while the powers of B they start with exponent 0 in the first and go up to N in the last: with this it can be said that in each of the terms the sum of the exponents is N.

As for the coefficients, it can be said that the coefficient of the first term is one and that of the second is N, and to determine a coefficient value, the theory of Pascal's triangles is usually applied.

With what has been said, it is enough to understand that the generalization of the square of the binomial works as follows:

(A + B)² = A² + 2 * A * B + B²

Examples of square binomial resolutions

1. (X + 1)² = X² + 2X + 1
2. (X-1)² = X² - 2X + 1
3. (3+6)² = 81
4. (4B + 3C)² = 16B² + 24BC + 9C²
5. (56-36)² = 400
6. (3/5 A + ½ B)² = 9/25 A² + ¼ B²
7. (2 * A² + 5 * B²)² = 4A⁴ + 25B ⁴
8. (10000-1000)² = 9000²
9. (2A - 3B)² = 4A² - 12AB + 9B²
10. (5ABC-5BCD)² = 25A² - 25D²
11. (999-666)² = 333²
12. (A-6)² = A² - 12A +36
13. (8a2b + 7ab6y²) ² = 64a4b² + 112a3b7y² + 49a²b12y4
14. (TO³+ 4B²)² = A⁶ + 8A³B² + 16A⁴
15. (1.5xy² + 2.5xy) ² = 2.25 x²y4 + 7.5x³y³ + 6.25x4y²
16. (3x - 4)² = 9x² - 24x - 16
17. (x - 5)² = x² -10x + 25
18. - (x - 3)² = -x²+ 6x-9
19. (3x⁵ + 8)² = 9x¹⁰ + 48x⁵ + 64