 |
| (1A)a | $\begin{align}&2x^2+3x+1\\[5pt]
=&2x^2+2x+1x+1\\[5pt]
=&2x(x+1)+1(x+1)\\[5pt]
=&\underline{\underline{(x+1)(2x+1)}}
\end{align}$ | b | $\begin{align}&5a^2-7a+2\\[5pt]
=&5a^2-5a-2a+2\\[5pt]
=&5a(a-1)-2(a-1)\\[5pt]
=&\underline{\underline{(a-1)(5a-2)}}
\end{align}$ | c | $\begin{align}&2x^2-x-1\\[5pt]
=&2x^2-2x+1x-1\\[5pt]
=&2x(x-1)+1(x-1)\\[5pt]
=&\underline{\underline{(x-1)(2x+1)}}
\end{align}$ |
| d | $\begin{align}&4p^2+4p-3\\[5pt]
=&4p^2+6p-2p-3\\[5pt]
=&2p(2p+3)-1(2p+3)\\[5pt]
=&\underline{\underline{(2p+3)(2p-1)}}
\end{align}$ | e | $\begin{align}&6x^2+3x-3\\[5pt]
=&6x^2+6x-3x-3\\[5pt]
=&6x(x+1)-3(x+1)\\[5pt]
=&(x+1)(6x-3)\\[5pt]
=&3(x+1)(2x-1)\\[5pt]
=&\underline{\underline{3(2x^2+x-1)}}
\end{align}$ | f | $\begin{align}&2x^2-11xy+15y^2\\[5pt]
=&2x^2-6xy-5xy+15y^2\\[5pt]
=&2x(x-3y)-5y(x-3y)\\[5pt]
=&\underline{\underline{(x-3y)(2x-5y)}}
\end{align}$ |
| g | $\begin{align}&2y^2-5ya+3a^2\\[5pt]
=&2y^2-3ay-2ay+3a^2\\[5pt]
=&y(2y-3a)-a(2y-3a)\\[5pt]
=&\underline{\underline{(2y-3a)(y-a)}}
\end{align}$ | h | $\begin{align}&2a^2+7ab+6b^2\\[5pt]
=&2a^2+4ab+3ab+6b^2\\[5pt]
=&2a(a+2b)+3b(a+2b)\\[5pt]
=&\underline{\underline{(a+2b)(2a+3b)}}
\end{align}$ | i | $\begin{align}&5p^2-9pq-2q^2\\[5pt]
=&5p^2-10pq+1pq-2q^2\\[5pt]
=&5p(p-2q)+q(p-2q)\\[5pt]
=&\underline{\underline{(p-2q)(5p+q)}}
\end{align}$ |
| j | $\begin{align}&2m^2+3mn-2n^2\\[5pt]
=&2m^2+4mn-1mn-2n^2\\[5pt]
=&2m(m+2n)-n(m+2n)\\[5pt]
=&\underline{\underline{(m+2n)(2m-n)}}
\end{align}$ | k | $\begin{align}&x^2y^2+10xy+16\\[5pt]
=&x^2y^2+8xy+2xy+16\\[5pt]
=&xy(xy+8)+2(xy+8)\\[5pt]
=&\underline{\underline{(xy+8)(xy+2)}}
\end{align}$ | l | $\begin{align}&2x^3-x^2y-3xy^2\\[5pt]
=&x(2x^2-xy-3y^2)\\[5pt]
=&x(2x^2-3xy+2xy-3y^2)\\[5pt]
=&x[x(2x-3y)+y(2x-3y)\\[5pt]
=&\underline{\underline{(2x-3y)(x+y)}}
\end{align}$ |
 |
| (2)a | $\begin{align}&8^2+7\times8+10\\[5pt]
=&x^2+7x+10\\[5pt]
=&x^2+5x+2x+10\\[5pt]
=&x(x+5)+2(x+5)\\[5pt]
=&(x+5)(x+2)\\[5pt]
=&(8+5)(8+2)\\[5pt]
=&(13)\times(10)\\[5pt]
=&\underline{\underline{130}}
\end{align}$ | b | $\begin{align}&93^2+3\times93-28\\[5pt]
=&y^2+3y-28\\[5pt]
=&y^2+7y-4y-28\\[5pt]
=&y(y+7)-4(y+7)\\[5pt]
=&(y+7)(y-4)\\[5pt]
=&(93+7)(93-4)\\[5pt]
=&(100)\times(89)\\[5pt]
=&\underline{\underline{8900}}
\end{align}$ | | |
| c | $\begin{align}&27^2-4\times27-21\\[5pt]
=&a^2-4a-21\\[5pt]
=&a^2-7a+3a-21\\[5pt]
=&a(a-7)+3(a-7)\\[5pt]
=&(a-7)(a+3)\\[5pt]
=&(27-7)(27+3)\\[5pt]
=&(20)\times(30)\\[5pt]
=&\underline{\underline{600}}
\end{align}$ | d | $\begin{align}&54^2+2\times54-24\\[5pt]
=&b^2+2b-24\\[5pt]
=&b^2+6b-4b-24\\[5pt]
=&b(b+6)-4(b+6)\\[5pt]
=&(b+6)(b-4)\\[5pt]
=&(54+6)(54-4)\\[5pt]
=&(60)\times(50)\\[5pt]
=&\underline{\underline{3000}}
\end{align}$ | | |
By studying this lesson you will be able to
Find the factors of trinomial quadratic expressions, find the factors of the difference of two squares.