Lesson EXAMPLES - Factoring
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<b>FACTORISATION EXAMPLES</b> Factorise the following: 1. {{{2xy - 12y}}} Visualise this as 2*x*y - 2*6*y. What is common to both terms? Answer is 2. What is left in both terms once the 2 is removed? Answer is xy - 6y --> answer is: 2(xy - 6y) ------------------------------------------------------------------------------------- 2. {{{5m^2 + 10mn}}} Visualise this as 5*m*m + 5*2*m*n What is common to both terms? Answer is 5*m What is left in both terms once the 2 is removed? Answer is m + 2*n --> answer is: 5m(m + 2n) ------------------------------------------------------------------------------------- 3. {{{6x^5 - 3xy^2 + 9x^2}}} Visualise this as 3*2*x*x*x*x*x - 3*x*y*y + 3*3*x*x What is common to both terms? Answer is 3*x What is left in both terms once the 2 is removed? Answer is 2*x*x*x*x - y*y + 3*x --> answer is: {{{ 3x(2x^4 - y^2 + 3x) }}} ------------------------------------------------------------------------------------- 4. {{{x^4y^3 - x^3y^2 + x^2y^5}}} Visualise this as x*x*x*x*y*y*y - x*x*x*y*y + x*x*y*y*y*y*y What is common to both terms? Answer is x*x*y*y What is left in both terms once the 2 is removed? Answer is x*x*y - x + y*y*y --> answer is: {{{ x^2y^2(x^2y - x + y^3) }}} ------------------------------------------------------------------------------------- 5. {{{ab^2c^2 + a^2b^3c^2 - a^4b^2c + a^5b^4c^3}}} Visualise this as a*b*b*c*c + a*a*b*b*b*c*c - a*a*a*a*b*b*c + a*a*a*a*a*b*b*b*b*c*c*c What is common to both terms? Answer is a*b*b*c What is left in both terms once the 2 is removed? Answer is c + a*b*c - a*a*a + a*a*a*a*b*b*c*c --> answer is: {{{ ab^2c(c + abc - a^3 + a^4b^2c^2) }}} ------------------------------------------------------------------------------------- <b>Summary</b> You will not get harder versions of factorisations of this type than these. The skill is to just look at the question and figure it out without writing the terms in the long-winded expanded versions I used above...the "Visualise" part. I only showed you this to explain what the terms actually mean and how to think about "common factors". All this comes with <b>practice</b> and <b>understanding such things as powers/exponents</b>.
