Question
26) \( (3 x+2 y)^{2}= \) 27) \( (4 a-3 b)^{2}= \) 28) \( (2 m+5 n)^{2}= \) 29) \( (3 p-q)^{2}= \) 30) \( (x+y+z)^{2}=x^{2}+y^{2}+z^{2} \) 11. \( (x+4)(x-4) \) 12. \( (3 y+2)(3 y-2) \) 13. \( (5 a+7)(5 a-7) \) 14. \( (2 m+n)(2 m-n) \)
Ask by Burton Bolton. in Mexico
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Desarrollos de las expresiones:
26) (3x + 2y)² = 9x² + 12xy + 4y²
27) (4a − 3b)² = 16a² − 24ab + 9b²
28) (2m + 5n)² = 4m² + 20mn + 25n²
29) (3p − q)² = 9p² − 6pq + q²
30) (x + y + z)² = x² + y² + z² + 2xy + 2xz + 2yz
11) (x + 4)(x − 4) = x² − 16
12) (3y + 2)(3y − 2) = 9y² − 4
13) (5a + 7)(5a − 7) = 25a² − 49
14) (2m + n)(2m − n) = 4m² − n²
Solution
Aquí tienes las desarrollos de las expresiones solicitadas:
26) (3x + 2y)²
= (3x)² + 2·(3x)(2y) + (2y)²
= 9x² + 12xy + 4y²
27) (4a − 3b)²
= (4a)² − 2·(4a)(3b) + (3b)²
= 16a² − 24ab + 9b²
28) (2m + 5n)²
= (2m)² + 2·(2m)(5n) + (5n)²
= 4m² + 20mn + 25n²
29) (3p − q)²
= (3p)² − 2·(3p)(q) + (q)²
= 9p² − 6pq + q²
30) (x + y + z)²
= x² + y² + z² + 2xy + 2xz + 2yz
Ahora las siguientes utilizando el producto de conjugados:
11) (x + 4)(x − 4)
= x² − 4²
= x² − 16
12) (3y + 2)(3y − 2)
= (3y)² − 2²
= 9y² − 4
13) (5a + 7)(5a − 7)
= (5a)² − 7²
= 25a² − 49
14) (2m + n)(2m − n)
= (2m)² − n²
= 4m² − n²
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
For the first set of expressions, you can use the formula for the square of a binomial, which is \( (a + b)^2 = a^2 + 2ab + b^2 \). For instance, in \( (3x + 2y)^2 \), this expands to \( 9x^2 + 12xy + 4y^2 \). The same approach works for all given squares! When you see the format \( (a+b)(a-b) \), it's the difference of squares! Using the formula \( (a+b)(a-b) = a^2 - b^2 \) helps simplify these: for example, \( (x+4)(x-4) \) equals \( x^2 - 16 \). Remember to identify a and b correctly for quick calculations!
