Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.4 - Page 61: 86

$-x^2-8x-47$

$$(3x+5)(2x-9)-(7x-2)(x-1)$$ Use the FOIL method (First, Outer, Inner, Last) to multiply each set of binomials: $$=[(3x\times 2x)+(3x\times (-9))+(5\times 2x)+(5\times (-9))]-[(7x\times x)+(7x\times (-1))+(-2\times x)+(-2\times (-1))]$$ $$=(6x^2-27x+10x-45)-(7x^2-7x-2x+2)$$ Combine like terms: $$=(6x^2-17x-45)-(7x^2-9x+2)$$ Distribute the negative: $$=6x^2-17x-45-7x^2+9x-2$$ Combine like terms: $$=-x^2-8x-47$$