The factorized form of \({x^2}-196\) is \(\boxed{\left({x - 14}\right)\left({x + 14}\right)}\).
The factorized form of \(9{x^2}-64\) is \(\boxed{\left({3x - 8}\right)\left({3x + 8}\right)}\) .
The factorized form of \(49{x^2}-56x+16\) is \(\boxed{{{\left({7x - 4}\right)}^2}}\) .
Further explanation:
The formula of \({a^2}-{b^2}\) can be written as,
\(\boxed{{a^2}-{b^2}=\left({a + b}\right)\left({a - b}\right)}\)
The formula of \({a^2}-2ab+{b^2}\) can be written as,
\(\boxed{{a^2}-2ab+{b^2}={{\left({a - b}\right)}^2}}\)
Given:
The equations are as follows.
1. \({x^2}-196\)
2. \(9{x^2}-64\)
3. \(49{x^2}-56x+16\)
Explanation:
(1)
The factorized form of the equation \(P\left(x\right)={x^2}-196\) can be obtained by solving the equation using the formula \(\boxed{{a^2}-{b^2}=\left({a + b}\right)\left({a - b}\right)}\).
The factorized form of \({x^2}-196\) is \(\boxed{\left({x-14}\right)\left({x + 14}\right)}\).
(2)
The factorized form of the equation \(Q\left(x\right)=9{x^2}-64\) can be obtained by solving the equation using the formula \(\boxed{{a^2}-{b^2}=\left({a+b}\right)\left({a-b}\right)}\).
\(\begin{aligned}Q\left(x\right)&=9{x^2}-64\\&={\left({3x}\right)^2}-{\left(8\right)^2}\\&=\left({3x+8}\right)\left({3x-8}\right)\\\end{aligned}\)
The factorized form of \(9{x^2}-64\) is \(\boxed{\left({3x-8}\right)\left({3x+8}\right)}\).
(3)
The factorized form of the equation \(R\left(x\right)=49{x^2}-56x+16\) can be obtained by solving the equation using the formula \(\boxed{{a^2}-2ab+{b^2}={{\left({a-b}\right)}^2}}\).
\(\begin{aligned}R\left(x\right)&=49{x^2}-56x+16\\&={\left({7x}\right)^2}-2\left({7x}\right)\left(4\right)+{\left(4\right)^2}\\&={\left({7x+4}\right)^2}\\\end{aligned}\)
The factorized form of \(49{x^2}-56x+16\) is \(\boxed{{{\left({7x-4}\right)}^2}}\).
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
