Respuesta :
Q1. The answer is (x – 14)(x + 14)
x² - 196 = x² - 14²
a² - b² = (a - b)(a + b)
a = x, b = 14
x² - 196 = x² - 14² = (x - 14)(x + 14)
Q2. The answer is (3x - 8)(3x + 8)
9x² - 64 = (3x)² - 8²
a² - b² = (a - b)(a + b)
a = 3x, b = 8
9x² - 64 = (3x)² - 8² = (3x - 8)(3x + 8)
Q3. The answer is (7x - 4)²
49x² - 56x + 16 = (7x)² - 2 * 7x * 4 + 4²
(a - b)² = a² - 2ab + b²
a = 7x, b = 4
49x² - 56x + 16 = (7x)² - 2 * 7x * 4 + 4² = (7x - 4)²
x² - 196 = x² - 14²
a² - b² = (a - b)(a + b)
a = x, b = 14
x² - 196 = x² - 14² = (x - 14)(x + 14)
Q2. The answer is (3x - 8)(3x + 8)
9x² - 64 = (3x)² - 8²
a² - b² = (a - b)(a + b)
a = 3x, b = 8
9x² - 64 = (3x)² - 8² = (3x - 8)(3x + 8)
Q3. The answer is (7x - 4)²
49x² - 56x + 16 = (7x)² - 2 * 7x * 4 + 4²
(a - b)² = a² - 2ab + b²
a = 7x, b = 4
49x² - 56x + 16 = (7x)² - 2 * 7x * 4 + 4² = (7x - 4)²
The factorized form of [tex]{x^2}-196[/tex] is [tex]\boxed{\left({x - 14}\right)\left({x + 14}\right)}[/tex].
The factorized form of [tex]9{x^2}-64[/tex] is [tex]\boxed{\left({3x - 8}\right)\left({3x + 8}\right)}[/tex] .
The factorized form of [tex]49{x^2}-56x+16[/tex] is [tex]\boxed{{{\left({7x - 4}\right)}^2}}[/tex] .
Further explanation:
The formula of [tex]{a^2}-{b^2}[/tex] can be written as,
[tex]\boxed{{a^2}-{b^2}=\left({a + b}\right)\left({a - b}\right)}[/tex]
The formula of [tex]{a^2}-2ab+{b^2}[/tex] can be written as,
[tex]\boxed{{a^2}-2ab+{b^2}={{\left({a - b}\right)}^2}}[/tex]
Given:
The equations are as follows.
1. [tex]{x^2}-196[/tex]
2. [tex]9{x^2}-64[/tex]
3. [tex]49{x^2}-56x+16[/tex]
Explanation:
(1)
The factorized form of the equation [tex]P\left(x\right)={x^2}-196[/tex] can be obtained by solving the equation using the formula [tex]\boxed{{a^2}-{b^2}=\left({a + b}\right)\left({a - b}\right)}[/tex].
The factorized form of [tex]{x^2}-196[/tex] is [tex]\boxed{\left({x-14}\right)\left({x + 14}\right)}[/tex].
(2)
The factorized form of the equation [tex]Q\left(x\right)=9{x^2}-64[/tex] can be obtained by solving the equation using the formula [tex]\boxed{{a^2}-{b^2}=\left({a+b}\right)\left({a-b}\right)}[/tex].
[tex]\begin{aligned}Q\left(x\right)&=9{x^2}-64\\&={\left({3x}\right)^2}-{\left(8\right)^2}\\&=\left({3x+8}\right)\left({3x-8}\right)\\\end{aligned}[/tex]
The factorized form of [tex]9{x^2}-64[/tex] is [tex]\boxed{\left({3x-8}\right)\left({3x+8}\right)}[/tex].
(3)
The factorized form of the equation [tex]R\left(x\right)=49{x^2}-56x+16[/tex] can be obtained by solving the equation using the formula [tex]\boxed{{a^2}-2ab+{b^2}={{\left({a-b}\right)}^2}}[/tex].
[tex]\begin{aligned}R\left(x\right)&=49{x^2}-56x+16\\&={\left({7x}\right)^2}-2\left({7x}\right)\left(4\right)+{\left(4\right)^2}\\&={\left({7x+4}\right)^2}\\\end{aligned}[/tex]
The factorized form of [tex]49{x^2}-56x+16[/tex] is [tex]\boxed{{{\left({7x-4}\right)}^2}}[/tex].
Learn more:
1. Learn more about inverse of the function https://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: polynomials
Keywords: quadratic equation, equation factorization. Factorized form, polynomial, quadratic formula, zeroes
