2. Sample Papers
  3. 8th Class
  4. Mathematics

8th Class Mathematics Sample Paper Mathematics Sample Paper - 2

  • question_answer
    Find the following square by using the identities
    (a) \[{{(b-7)}^{2}}\]
    (b) \[{{(xy+3z)}^{2}}\]
    (c) \[{{(6{{x}^{2}}-5y)}^{2}}\]
    (d) \[{{\left( \frac{2}{3}m+\frac{3}{2}n \right)}^{2}}\]
    (e) \[{{(0.4p-0.5q)}^{2}}\]
    (f) \[{{(2xy+5y)}^{2}}\]

    Answer:

    (a) \[{{(b7)}^{2}}\]
    Use the identity,
                                                         \[{{(ab)}^{2}}={{a}^{2}}2ab+{{b}^{2}}\]
                                             \[={{b}^{2}}2(b)(7)+{{\left( 7 \right)}^{2}}\]
                                                                          \[={{b}^{2}}14b+\text{ }49\]
    (b) \[{{(xy+3z)}^{\mathbf{2}}}\]
    Use the identity,
                  \[{{(a+b)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}={{(xy)}^{2}}+2(xy)(3z)+{{(3z)}^{2}}\]
                                             \[={{x}^{2}}{{y}^{2}}+6xyz+9{{z}^{2}}\]
    (c)
                                                                        \[{{(6{{x}^{2}}5y)}^{2}}={{(6x)}^{2}}2(6x)(5y)+{{(5y)}^{2}}\]
    Use the identity,
                                                         \[{{(ab)}^{2}}={{a}^{2}}2ab+{{b}^{2}}\]
                                                           \[=36{{x}^{4}}12x\times 5y+25{{y}^{2}}\]
                                                                                                \[=\text{ }36{{x}^{4}}60{{x}^{2}}y+25{{y}^{2}}\]
    (d)
                                         \[{{\left( \frac{2}{3}m+\frac{3}{2}n \right)}^{2}}\]
    Use the identity,
                                                      \[{{(a+b)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}\]
               \[={{\left( \frac{2}{3}m \right)}^{2}}+2\left( \frac{2}{3}m \right)\left( \frac{3}{2}n \right)+{{\left( \frac{3}{2}n \right)}^{2}}\]
    \[=\frac{4}{9}{{m}^{2}}+\frac{4}{3}m\left( \frac{3}{2}n \right)+{{\left( \frac{9}{4}n \right)}^{2}}\]
                                                      \[=\frac{4}{9}{{m}^{2}}+2mn+\frac{9}{4}{{n}^{2}}\]
    (e)
                                                                                                                                                        \[{{(0.4p0.5q)}^{2}}\]
    Use the identity,
                                                         \[{{(ab)}^{2}}={{a}^{2}}2ab+{{b}^{2}}\]
                     \[={{(0.4p)}^{2}}2\text{ }\left( 0.4 \right)\left( 0.5 \right)\text{ }(p\times q)+{{(0.5q)}^{2}}\]
                       \[=0.16{{p}^{2}}\text{ }\left( 0.8 \right)\left( 0.5 \right)pq+0.25{{q}^{2}}\]
                                                                \[=0.16{{p}^{2}}0.40pq+0.25{{q}^{2}}\]
    (f)
                                                                                                                                                          \[{{(2xy+5y)}^{2}}\]
    Use the identity,
                                                                                                        \[{{(a+b)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}\]
                                              \[={{(2xy)}^{2}}+\text{ }2(2xy)\text{ }(5y)+{{(5y)}^{2}}\]
                                           \[=\text{ }4{{x}^{2}}{{y}^{2}}+4xy\times 5y+25{{y}^{2}}\]
                                         \[=\text{ }4{{x}^{2}}{{y}^{2}}+\text{ }20x{{y}^{2}}+25{{y}^{2}}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner