y-7xy+5-35x factoring by grouping a polynomial rs+as+br+ab """""""""""""""""""""m²+2mn+n²-495x+10y-3x²-6xy
Answer (1)
Step-by-step explanation:Let's factor each of the given polynomials by grouping.1. ( y - 7xy + 5 - 35x ): Group the terms as follows: (y - 7xy) + (5 - 35x) Factor out the common factors from each group: y(1 - 7x) + 5(1 - 7x) Factor out the common binomial factor (1 - 7x): (1 - 7x)(y + 5) 2. ( rs + as + br + ab ): Group the terms: (rs + as) + (br + ab) Factor out the common factors: s(r + a) + b(r + a) Factor out the common binomial factor (r + a): (r + a)(s + b) 3. ( m² + 2mn + n² - 49 ): Notice that the first three terms are a perfect square trinomial and the last term is a difference of squares: (m² + 2mn + n²) - 49 Factor the perfect square trinomial: (m + n)² - 49 Factor the difference of squares: (m + n - 7)(m + n + 7) 4. ( 5x + 10y - 3x²- 6xy \): Group the terms: (5x + 10y) - (3x² + 6xy) Factor out the common factors: 5(x + 2y) - 3x(x + 2y) Factor out the common binomial factor (x + 2y): (x + 2y)(5 - 3x) These are the factored forms of the given polynomials.
